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BLACKFORD COUNTY SCHOOLS

FOURTH GRADE CURRICULUM MAP

(USING SAXON BOOK)

http://www.bcs.k12.in.us/Home

Result Unknown Change Unknown Start Unknown

Add to

Two bunnies sat on the grass. Three more bunnies hopped there. How

many bunnies are on the grass now?

2 + 3 = ?

Two bunnies were sitting on the grass. Some more bunnies hopped there. Then there were five bunnies. How many bunnies hopped over to

the first two?

2 + ? = 5

Some bunnies were sitting on the grass. Three more bunnies hopped there. Then there were five bunnies. How many bunnies were on the grass

before?

? + 3 = 5

Take from

Five apples were on the table. I ate two apples. How many apples are on

the table now?

5 – 2 = ?

Five apples were on the table. I ate some apples. Then there were three apples. How many apples did I eat?

5 - ? = 3

Some apples were on the table. I ate two apples. Then there were three apples. How many apples

were on the table before?

? – 2 = 3

Total Unknown Addend Unknown Both addends Unknown

Put Together/ Take Apart

Three red apples and two green apples are on the table. How many

apples are on the table?

3 + 2 = ?

Five apples are on the table. Three are red and the rest are green. How

many apples are green?

3 + ? = 5, 5 – 3 = ?

Grandma has five flowers. How many can she put in her red vase and how many in her blue vase? 5 = 0 + 5, 5 = 5 + 0 5 = 1 + 4, 5 + 4 + 1 5 = 2 + 3, 5 = 3 + 2 Difference Unknown

Bigger Unknown

Smaller Unknown

Difference Unknown Bigger Unknown Smaller Unknown

Compare

(“How many more?” version): Lucy has two apples. Julie has five apples. How many more apples does Julie have than Lucy? (“How many fewer?” version): Lucy has two apples. Julie has five apples. How may fewer apples does Lucy have than Julie? 2 + ? = 5, 5 – 2 = ?

(Version with “more”): Julie has 3 more apples than Lucy. Lucy has two apples. How many

apples does Julie have? (Version with “fewer”):

Lucy has three fewer apples than Julie. Lucy has two apples. How many apples does Julie have?

2 + 3 = ?, 3 + 2 = ?

Julie has three more apples than Lucy. Julie has five apples. How many apples does Lucy have?

(Version with “fewer”): Lucy has three fewer apples than Julie. Julie has five apples. How many apples does Lucy have?

5 – 3 = ?, ? + 3 = 5

Addition Strategies Name Clarification Work Sample

Counting All

• Student counts every number • Students are not yet able to add on from either addend, they must mentally build every number

8 + 9 1,2,3,4,5,6,7,8,9,10,11,12,13

Counting On

• Transitional strategy • Student starts with 1 number and counts on from this point

8 + 9 8…9,10,11,12,13,14,15

Doubles/

Near Doubles

• Student recalls sums for many doubles 8 + 9 8 + (8 + 1) (8 + 8) + 1 16 + 1 = 17

Making Tens

• Student uses fluency with ten to add quickly 8 + 9 (7 + 1) + 9 7 + (1 + 9) 7 + 10 = 17

Making Friendly

Numbers/ Landmark Numbers

• Friendly numbers are numbers that are easy to use in mental computation • Student adjusts one or all addends by adding or subtracting to make friendly numbers • Student then adjusts the answer to compensate

23 + 48 23 + (48 + 2) 23 + 50 = 73 73 -2 =71

Compensation

• Student manipulates the numbers to make them easier to add • Student removes a specific amount from one addend and gives that exact amount to the other addend

8 + 6 8 -1 =7 6 + 1 = 7 7 + 7 =14

Breaking Each

Number into its Place Value

• Strategy used as soon as students understand place value • Student breaks each addend into its place value (expanded notations) and like place value amounts are

combined • Student works left to right to maintain the magnitude of the numbers

24 + 38 (30 + 4) + (30 + 8) 20 + 30 = 50 4 + 8 = 12 50 + 12 = 62

Adding up in

Chunks

• Follows place value strategy • Student keeps one addend whole and adds the second addend in easy to use chunks • More efficient than place value strategy because student is only breaking apart one addend

45 + 28 45 + ( 20 + 8) 45 + 20 = 65 65 + 8 = 73

Subtraction Strategies

Name Clarification Sample

Adding up

• Student adds up from the number being subtracted to the whole • The larger the jumps, the more efficient the strategy • Student uses knowledge of basic facts, doubles, making ten, and counting on

14 – 7 7… 8,9,10,11,12,13,14 (+1 each jump)

7 + 3= 10 10 + 4= 14

Counting Back

• Strategy used by students who primarily view subtraction as taking away • Student starts with the whole and removes the subtracting in parts • Student needs the ability to decompose numbers in east to remove parts

65 – 32 65 – (10 + 10 + 10 + 2) 65, 55, 45, 35, 33 65 – (30 + 2) 65 – 30 = 35 35 – 2 = 33

Place Value

• Student breaks each number into its place value (expanded notation) • Student groups like place values and subtracts

999 – 345 (900 + 90 + 9) – (300 + 40 + 5) 900 – 300 = 600 90 – 40 = 50 9 – 5 = 4 600 + 50 + 4 = 654

Keeping a Constant

Difference

• Student understands that adding or subtracting the same amount from both numbers maintains the distance between the numbers

• Student manipulates the numbers to create friendlier numbers

123 – 59 123 + 1 = 124 59 + 1 = 60 124 – 60 = 64

Adjusting the

Create and Easier Number

• Strategy requires students to adjust only one of the numbers in a subtraction problem

• Student chooses a number to adjust, subtracts, then adjusts the final answer to compensate

• Students must understand part/whole relationships to reason through this strategy

123 – 59 59 + 1 = 60 123 – 60 = 63 I added 1 to make an easier number. 63 + 1 = 64 I have to add 1 to my final answer because I took away 1 too many.

Common Multiplication and Division Situations

Unknown Product 3 X 6 = ?

Group Size Unknown (How many in each group)

Number of Groups Unknown (How many groups?)

Equal Groups

There are 3 bags with 6 plums in each bag. How many plums are there in all? Measurement example: You need 3 lengths of string, each 6 inches long. How much string will you need altogether?

If 18 plums are shared equally into 3 bags, then how many plums will be in each bag? Measurement example: You have 18 inches of string, which you will cut into 3 equal pieces. How long will each piece of string be?

If 18 plums are to be packed 6 to a bag, then how many bags are needed? Measurement example: You have 18 inches of string, which you will cut into pieces that are 6 inches long. How many pieces of string will you have?

Arrays, Area

There are 3 rows of apples with 6 apples in each row. How many apples are there? Area example: What is the area of a 3 cm by 6cm rectangle?

If 18 apples are arranged into 3 equal rows, how may apples will be in each row? Area example: A rectangle has area 18 square centimeters. If one side is 3 cm long, how long is a side next to it?

If 18 apples are arranged into equal rows of 6 apples, how many rows will there be? Area example: A rectangle has area 18 square centimeters. If one side is 6cm long, how long is a side next to it?

Compare

A blue hat costs $6. A red hat cost 3 times as much as the blue hat. How much does the red hat cost? Measurement example: A rubber band is 6 cm long. How long will the rubber band be when it is stretched to be 3 times as long?

A red hat costs $18 and that is 3 times as much as a blue hat costs. How much does the blue bat cost? Measurement example: A rubber band is stretched to be 18 cm long and that is 3 times as long as it was at first. How long was the rubber band at first?

A red hat costs $18 and a blue hat costs $6. How many times as much does the red hat cost as the blue hat? Measurement example: A rubber band was 6 cm long at first. Now it is stretched to be 18 cm long. How many times as long is the rubber band now as it was at first?

General a x b = ? a x ? = p and p ÷ a = ? ? x b = p and p ÷ b =?

Multiplication Strategies Name Clarification Student Work Sample

Repeated Addition/Skip

Counting

• Beginning strategy for students who are just learning multiplication • Connection to an array model provides an essential visual model

6 × 15 15+15+15+15+15+15 = 90 2 × 15 = 30 2 × 15 = 30 2 × 15 = 30 30 + 30 + 30 = 90

Friendly Numbers/Landmark

Numbers

• Students who are comfortable multiplying by multiples of 10 9 × 15 Add 1 group of 15 10 × 15 = 150 We must now take off 1 group of 15. 150 – 15 = 135

Partial Products

• strategy based on the distributive property and is the precursor for our standard U.S. algorithm

• student must understand that the factors in a multiplication problem can be broken into addends

• student can then u se friendlier numbers to solve more difficult problems

12 × 15 12 × (10 + 5) 12 × 10 = 120 12 × 5 = 60 120 + 60 =180

Breaking Factors into Smaller Factors

• Strategy relies on students’ understand of breaking factors into smaller factors

• Associate property

12 × 25 (3 × 4) × 25 3 × (4 × 25) (4 × 25) + (4 × 25) + (4 × 25) = 300

Doubling and

Halving

• Used by students who have an understanding of the concept of arrays with different dimensions but the same area

• Student can double and halve numbers with ease • Student doubles one factor and halves the other factor

8 × 25 8÷2 = 4 25 × 2 = 50 4 × 50 = 200

Division Strategies Name Clarification Student Work Sample

Repeated Subtraction/Sharing

• Early strategy students use when they are developing multiplicative reasoning

• Repeated subtraction is one of the least efficient division strategies

• Presents opportunities to make connections to multiplication

30 ÷ 5 30 – 5 = 25 25 – 5 = 20 20 = 5 = 15 15 – 5 = 10 10 – 5 = 5 5 – 5 = 0 I took out 6 groups of 5 30 ÷ 5 = 6

Multiplying Up

• Strategy is a natural progression from repeated subtraction • Student uses strength in multiplication to multiply up to reach the

dividend • Students relying on smaller factors and multiples will benefit from

discussions related to choosing more efficient factors

384 ÷ 16 10 × 16 = 160 384 – 160 = 224 10 × 16 = 160 224 – 160 = 64 2 × 16 = 32 64 – 32 = 32 2 × 16 = 32 32 – 32 = 0 10 + 10 + 2 + 2 = 24

Partial Quotients

• Maintains place value • Allows students to work their way toward the quotient by using

friendly numbers such as ten, five, and two • As the student chooses larger numbers, the strategy becomes

more efficient

384 ÷ 16 _____ 16) 384 -160 224 -160 64 -32 32 -32 0

Proportional

Reasoning

• Students who have a strong understand of factors, multiples, and fractional reasoning

• Students’ experiences with doubling and halving to solve multiplication problems can launch an investigation leading to the idea that you can divide the dividend and the divisor by the same number to create a friendlier problem

384 ÷ 16 384 ÷ 16 ÷2 ÷2 192 ÷ 8 ÷2 ÷2 96 ÷ 4 ÷2 ÷2 48 ÷ 2 = 24 384 ÷ 16 = 24

Problem Solving Strategies Focus

By Grade Level

Grade Level Strategies Kindergarten Use Objects First Review Previous Grades

Draw a Picture Use a Number Sentence

Second Review Previous Grades Find a Pattern Make a Table

Third Review Previous Grades Work Backwards Make It Simpler

Fourth Review Previous Grades Make an Organized List Guess and Check

Fifth Review Previous Grades Use Logical Reasoning

Sixth: Students should know all strategies that will be used all year.

2016-17 Pacing Guide: Quarter 1

Week 1 Sets: 1-2, 3,4,5

4.C.4: Multiply fluently within 100. 4.AT.1: Solve real-world problems involving addition and subtraction of multi-digit whole numbers (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). 4.NS.9: Use place value understanding to round multi-digit whole numbers to any given place value.

Week 2 Sets: 6,7,8,9

4.C.4: Multiply fluently within 100. 4.AT.1: Solve real-world problems involving addition and subtraction of multi-digit whole numbers (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). 4.C.1: Add and subtract multi-digit whole numbers fluently using a standard algorithmic approach. 4.NS.1: Read and write whole numbers up to 1,000,000. Use words, models, standard form and expanded form to represent and show equivalent forms of whole numbers up to 1,000,000. 4.M.3: Use the four operations (addition, subtraction, multiplication and division) to solve real-world problems involving distances, intervals of time, volumes, masses of objects, and money. Include addition and subtraction problems involving simple fractions and problems that require expressing measurements given in a larger unit in terms of a smaller unit.

Week 3 Sets: 10-16

4.C.4: Multiply fluently within 100. 4.AT.1: Solve real-world problems involving addition and subtraction of multi-digit whole numbers (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). 4.C.1: Add and subtract multi-digit whole numbers fluently using a standard algorithmic approach.

Week 4 Sets: 18, 19, 20, 25, 27b

4.C.4: Multiply fluently within 100. 4.M.3: Use the four operations (addition, subtraction, multiplication and division) to solve real-world problems involving distances, intervals of time, volumes, masses of objects, and money. Include addition and subtraction problems involving simple fractions and problems that require expressing measurements given in a larger unit in terms of a smaller unit. 4.AT.1: Solve real-world problems involving addition and subtraction of multi-digit whole numbers (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). 4.NS.9: Use place value understanding to round multi-digit whole numbers to any given place value. 4.NS.6: Write tenths and hundredths in decimal and fraction notations. Use words, models, standard form and expanded form to represent decimal numbers to hundredths. Know the fraction and decimal equivalents for halves and fourths (e.g., 1/2 = 0.5 = 0.50, 7/4 = 1 3/4 = 1.75).

Week 5 Sets: 22,23, 24,25

4.C.4: Multiply fluently within 100. 4.G.3: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint 4.AT.1: Solve real-world problems involving addition and subtraction of multi-digit whole numbers (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). 4.NS.3: Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers. Name and write mixed numbers using objects or pictures. Name and write mixed numbers as improper fractions using objects or pictures.

Week 6 Sets: 27, 28, 29, 30, 31, 32, 38

4.C.4: Multiply fluently within 100. 4.AT.1: Solve real-world problems involving addition and subtraction of multi-digit whole numbers (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem).

4.C.2: Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Describe the strategy and explain the reasoning

4.C.7: Show how the order in which two numbers are multiplied (commutative property) and how numbers are grouped in multiplication (associative property) will not change the product. Use these properties to show that numbers can by multiplied in any order. Understand and use the distributive property. 4.C.1: Add and subtract multi-digit whole numbers fluently using a standard algorithmic approach.

Week 7 Sets: 33,34,35, 36,37, 39, 40

4.C.4: Multiply fluently within 100. 4.NS.1: Read and write whole numbers up to 1,000,000. Use words, models, standard form and expanded form to represent and show equivalent forms of whole numbers up to 1,000,000. 4.NS.3: Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers. Name and write mixed numbers using objects or pictures. Name and write mixed numbers as improper fractions using objects or pictures. 4.M.3: Use the four operations (addition, subtraction, multiplication and division) to solve real-world problems involving distances, intervals of time, volumes, masses of objects, and money. Include addition and subtraction problems involving simple fractions and problems that require expressing measurements given in a larger unit in terms of a smaller unit. 4.M.1: Measure length to the nearest quarter-inch, eighth-inch, and millimeter.

Week 8 Sets: 41, 42, 43, 44, 50, 48

4.C.4: Multiply fluently within 100. 4.C.1: Add and subtract multi-digit whole numbers fluently using a standard algorithmic approach 4.AT.4: Solve real-world problems with whole numbers involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem), distinguishing multiplicative comparison from additive comparison. [In grade 4, division problems should not include a remainder.] 4.M.3: Use the four operations (addition, subtraction, multiplication and division) to solve real-world problems involving distances, intervals of time, volumes, masses of objects, and money. Include addition and subtraction problems involving simple fractions and problems that require expressing measurements given in a larger unit in terms of a smaller unit. 4.C.2: Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Describe the strategy and explain the reasoning.

Week 9 Sets: 45, 51a, 46, 51b, 47, 49, 52, 53

4.C.4: Multiply fluently within 100. 4.C.1: Add and subtract multi-digit whole numbers fluently using a standard algorithmic approach. 4.C.2: Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Describe the strategy and explain the reasoning. 4.C.7: Show how the order in which two numbers are multiplied (commutative property) and how numbers are grouped in multiplication (associative property) will not change the product. Use these properties to show that numbers can by multiplied in any order. Understand and use the distributive property. 4.NS.8: Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. 4.AT.2: Recognize and apply the relationships between addition and multiplication, between subtraction and division, and the inverse relationship between multiplication and division to solve real-world and other mathematical problems. 4.AT.4: Solve real-world problems with whole numbers involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem), distinguishing multiplicative comparison from additive comparison. [In grade 4, division problems should not include a remainder.] 4.C.3: Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Describe the strategy and explain the reasoning.


Week 10 Sets: 54, 55, 58

4.C.4: Multiply fluently within 100. 4.NS.9: Use place value understanding to round multi-digit whole numbers to any given place value. 4.NS.8: Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. 4.C.2: Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Describe the strategy and explain the reasoning.

Week 11 Sets: 56, 57, 60, 59, 61

4.C.4: Multiply fluently within 100. 4.AT.5: Solve real-world problems involving addition and subtraction of fractions referring to the same whole and having common denominators (e.g., by using visual fraction models and equations to represent the problem). 4.AT.4: Solve real-world problems with whole numbers involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem), distinguishing multiplicative comparison from additive comparison. [In grade 4, division problems should not include a remainder.]

Week 12 Sets: 62, 63, 64, 65, 66, 67, 85

4.C.4: Multiply fluently within 100. 4.C.2: Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Describe the strategy and explain the reasoning. 4.G.1: Identify, describe, and draw parallelograms, rhombuses, and trapezoids using appropriate tools (e.g., ruler, straightedge and technology). 4.G.5: Classify triangles and quadrilaterals based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles (right, acute, obtuse). 4.C.3: Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Describe the strategy and explain the reasoning.

Week 13 Sets: 68. 69, 70, 71

4.C.4: Multiply fluently within 100. 4.M.1: Measure length to the nearest quarter-inch, eighth-inch, and millimeter. 4.C.3: Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Describe the strategy and explain the reasoning. 4.AT.5: Solve real-world problems involving addition and subtraction of fractions referring to the same whole and having common denominators (e.g., by using visual fraction models and equations to represent the problem).

Week 14 Sets: 78, 79, 73, 82

4.C.4: Multiply fluently within 100. 4.G.5: Classify triangles and quadrilaterals based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles (right, acute, obtuse). 4.G.2: Recognize and draw lines of symmetry in two-dimensional figures. Identify figures that have lines of symmetry.

Week 15 Sets: 72, 74, 75, 77, 76, 80

4.C.4: Multiply fluently within 100. 4.DA.1: Formulate questions that can be addressed with data. Use observations, surveys, and experiments to collect, represent, and interpret the data using tables (including frequency tables), line plots, and bar graphs. 4.AT.5: Solve real-world problems involving addition and subtraction of fractions referring to the same whole and having common denominators (e.g., by using visual fraction models and equations to represent the problem). 4.G.4: Identify, describe, and draw rays, angles (right, acute, obtuse), and perpendicular and parallel lines using appropriate tools (e.g., ruler, straightedge and technology). Identify these in two-dimensional figures.

4.M.5: Understand that an angle is measured with reference to a circle, with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. Understand an angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure other angles. Understand an angle that turns through n one-degree angles is said to have an angle measure of n degrees. 4.C.3: Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Describe the strategy and explain the reasoning.

Week 16 Sets: 83, 84, 86, 87, 90

4.C.4: Multiply fluently within 100. 4.NS.9: Use place value understanding to round multi-digit whole numbers to any given place value. 4.C.2: Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Describe the strategy and explain the reasoning.

Week 17 Sets: 88, 89, 91, 93

4.C.4: Multiply fluently within 100. 4.C.3: Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Describe the strategy and explain the reasoning 4.NS.3: Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers. Name and write mixed numbers using objects or pictures. Name and write mixed numbers as improper fractions using objects or pictures. 4.NS.7: Compare two decimals to hundredths by reasoning about their size based on the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions (e.g., by using a visual model).

Week 18 Sets: 92, 94, 95, 99

4.C.4: Multiply fluently within 100. 4.G.1: Identify, describe, and draw parallelograms, rhombuses, and trapezoids using appropriate tools (e.g., ruler, straightedge and technology). 4.G.5: Classify triangles and quadrilaterals based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles (right, acute, obtuse). 4.NS.6: Write tenths and hundredths in decimal and fraction notations. Use words, models, standard form and expanded form to represent decimal numbers to hundredths. Know the fraction and decimal equivalents for halves and fourths (e.g., 1/2 = 0.5 = 0.50, 7/4 = 1 3/4 = 1.75).


Week 19 Sets: 98, 101, 100, 102, 103

4.C.4: Multiply fluently within 100. 4.DA.1: Formulate questions that can be addressed with data. Use observations, surveys, and experiments to collect, represent, and interpret the data using tables (including frequency tables), line plots, and bar graphs. 4.NS.6: Write tenths and hundredths in decimal and fraction notations. Use words, models, standard form and expanded form to represent decimal numbers to hundredths. Know the fraction and decimal equivalents for halves and fourths (e.g., 1/2 = 0.5 = 0.50, 7/4 = 1 3/4 = 1.75). 4.NS.5: Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark, such as 0, 1/2, and 1). Recognize comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions (e.g., by using a visual fraction model).

Week 20 Sets: 96, 97, 104, 107, 105, 111

4.C.4: Multiply fluently within 100. 4.DA.1: Formulate questions that can be addressed with data. Use observations, surveys, and experiments to collect, represent, and interpret the data using tables (including frequency tables), line plots, and bar graphs. 4.NS.3: Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers. Name and write mixed numbers using objects or pictures. Name and write mixed numbers as improper fractions using objects or pictures. 4.C.5: Add and subtract fractions with common denominators. Decompose a fraction into a sum of fractions with common denominators. Understand addition and subtraction of fractions as combining and separating parts referring to the same whole. 4.C.3: Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Describe the strategy and explain the reasoning. 4.M.4: Apply the area and perimeter formulas for rectangles to solve real-world problems and other mathematical problems. Recognize area as additive and find the area of complex shapes composed of rectangles by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts; apply this technique to solve real-world problems and other mathematical problems.

Week 21 Sets: 109, 112, 106, 108

4.C.4: Multiply fluently within 100. 4.NS.4: Explain why a fraction, a/b, is equivalent to a fraction, (n × a)/(n × b), by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. [In grade 4, limit denominators of fractions to 2, 3, 4, 5, 6, 8, 10, 25, 100.] 4.AT.1: Solve real-world problems involving addition and subtraction of multi-digit whole numbers (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). 4.AT.4: Solve real-world problems with whole numbers involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem), distinguishing multiplicative comparison from additive comparison. [In grade 4, division problems should not include a remainder.] 4.C.7: Show how the order in which two numbers are multiplied (commutative property) and how numbers are grouped in multiplication (associative property) will not change the product. Use these properties to show that numbers can by multiplied in any order. Understand and use the distributive property.

Week 22 Sets: 113, 117, 110, 114

4.C.4: Multiply fluently within 100. 4.C.3: Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Describe the strategy and explain the reasoning. 4.NS.9: Use place value understanding to round multi-digit whole numbers to any given place value. 4.NS.4: Explain why a fraction, a/b, is equivalent to a fraction, (n × a)/(n × b), by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. [In grade 4, limit denominators of fractions to 2, 3, 4, 5, 6, 8, 10, 25, 100.]

Week 23 Sets: 115, 116, 118

4.C.4: Multiply fluently within 100. 4.NS.4: Explain why a fraction, a/b, is equivalent to a fraction, (n × a)/(n × b), by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. [In grade 4, limit denominators of fractions to 2, 3, 4, 5, 6, 8, 10, 25, 100.] 4.NS.5: Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark, such as 0, 1/2, and 1). Recognize comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions (e.g., by using a visual fraction model). 4.NS.6: Write tenths and hundredths in decimal and fraction notations. Use words, models, standard form and expanded form to represent decimal numbers to hundredths. Know the fraction and decimal equivalents for halves and fourths (e.g., 1/2 = 0.5 = 0.50, 7/4 = 1 3/4 = 1.75). 4.C.3: Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Describe the strategy and explain the reasoning.

Week 24 Sets: 119, 120

4.C.4: Multiply fluently within 100. 4.C.5: Add and subtract fractions with common denominators. Decompose a fraction into a sum of fractions with common denominators. Understand addition and subtraction of fractions as combining and separating parts referring to the same whole. 4.C.6: Add and subtract mixed numbers with common denominators (e.g. by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction). 4.DA.2: Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using data displayed in line plots. 4.DA.1: Formulate questions that can be addressed with data. Use observations, surveys, and experiments to collect, represent, and interpret the data using tables (including frequency tables), line plots, and bar graphs.

Week 25 4.C.4: Multiply fluently within 100. 4.M.6: Measure angles in whole-number degrees using appropriate tools. Sketch angles of specified measure. 4.M.4: Apply the area and perimeter formulas for rectangles to solve real-world problems and other mathematical problems. Recognize area as additive and find the area of complex shapes composed of rectangles by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts; apply this technique to solve real-world problems and other mathematical problems. 4.M.6: Measure angles in whole-number degrees using appropriate tools. Sketch angles of specified measure.

Week 26 4.C.4: Multiply fluently within 100.


Weeks 1-3:

Problem Solving: Should be embedded within daily instruction:

Make sense of problems and persevere in

solving them.

PS.1

Reason

abstractly and quantitatively

PS.2

Construct viable arguments and

critique the reasoning of

others PS.3

Model with

Mathematics

PS.4

Use appropriate

tools strategically

PS.5

Attend to precision

PS.6

Look for and make sure of

structure

PS. 7

Look for and

express regularity in repeated reasoning.

PS.8

DOK (Depth of Knowledge) Level 1:

identify, list, label, illustrate, measure, state, tell, use, match

Level 2: graph, classify, cause/effect,

estimate, compare, infer, construct, summarize, interpret,

estimate

Level 3: Revise, critique, construct, investigate, cite evidence,

conclusions, assess

Level 4: Design, connect, synthesize, critique,

analyze, create, prove, apply concepts

Critical Standards (check plus) for 3 weeks: Spiral Review of Current Curriculum →

Week 1:

Benchmarks to be taught:

Activities

Vocabulary

Standards: 4.C.4: Multiply fluently within 100. 4.AT.1: Solve real-world problems involving addition and subtraction of multi-digit whole numbers (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). 4.NS.9: Use place value understanding to round multi-digit whole numbers to any given place value. 4.C.1: Add and subtract multi-digit whole numbers fluently using a standard algorithmic approach. 4.NS.1: Read and write whole numbers up to 1,000,000. Use words, models, standard form and expanded form to represent and show equivalent forms of whole numbers up to 1,000,000. 4.M.3: Use the four operations (addition, subtraction, multiplication and division) to solve real-world problems involving distances, intervals of time, volumes, masses of objects, and money. Include addition and subtraction problems involving simple fractions and problems that require expressing measurements given in a larger unit in terms of a smaller unit. (money only at this point) Students will:

• Solve problems with addition and subtraction • Use a symbol for an unknown number • Understand place value to round • Read numbers to 1,000,000 • Write numbers to 1,000,000 • Use standard form to represent whole numbers to show equivalent forms • Use expanded form to represent whole numbers to show equivalent forms • Add and subtract money appropriately

AIMS: Internet Resources:

Addends Addition Algorithmic approach Cent coins Difference Dollar Equivalent Expanded form Fluently Mass Models Operation Place value Represent Standard form Subtraction Sum Volume Whole numbers Word form

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&uact=8&ved=0ahUKEwi908q_n8XLAhWCm4MKHY_iCPwQjRwIBw&url=http://salk4thgrade.weebly.com/place-value.html&psig=AFQjCNFy1hNEtkkXRF3xnd2E1mDMHLCwfA&ust=1458219067885689

Week 2:


Activities

Vocabulary

Standards: 4.C.4: Multiply fluently within 100. 4.AT.1: Solve real-world problems involving addition and subtraction of multi-digit whole numbers (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). 4.C.1: Add and subtract multi-digit whole numbers fluently using a standard algorithmic approach. 4.M.3: Use the four operations (addition, subtraction, multiplication and division) to solve real-world problems involving distances, intervals of time, volumes, masses of objects, and money. Include addition and subtraction problems involving simple fractions and problems that require expressing measurements given in a larger unit in terms of a smaller unit. (money only at this point) Students will:

• Solve problems with addition and subtraction • Use a symbol for the unknown number • Use addition and subtraction for money


Addends Addition Algorithmic approach Cents Coins Different Dollars Drawings Equations Fluently Mass Subtraction Sum Symbol Unknown number Variable Volume Whole numbers

Week 3:


Activities

Vocabulary

Standards: 4.C.4: Multiply fluently within 100. 4.C.1: Add and subtract multi-digit whole numbers fluently using a standard algorithmic approach. 4.AT.1: Solve real-world problems involving addition and subtraction of multi-digit whole numbers (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). Students will:

• Add and subtract fluently • Solve problems involving addition and subtraction of whole numbers • Use symbols to represent the unknown number


Addends Addition Algorithmic approach Difference Equations Fluently Represent Subtraction Sum Symbols Unknown number Variable Whole numbers

Weeks 4-6:



solving them.

PS.1

Reason


PS.2



others PS.3

Model with

Mathematics

PS.4

Use appropriate

tools strategically

PS.5

Attend to precision

PS.6


structure

PS. 7

Look for and


PS.8





estimate


conclusions, assess




Week 4:


Activities

Vocabulary

Standards: 4.C.4: Multiply fluently within 100. 4.M.3: Use the four operations (addition, subtraction, multiplication and division) to solve real-world problems involving distances, intervals of time, volumes, masses of objects, and money. Include addition and subtraction problems involving simple fractions and problems that require expressing measurements given in a larger unit in terms of a smaller unit. 4.AT.1: Solve real-world problems involving addition and subtraction of multi-digit whole numbers (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). 4.NS.9: Use place value understanding to round multi-digit whole numbers to any given place value. 4.NS.6: Write tenths and hundredths in decimal and fraction notations. Use words, models, standard form and expanded form to represent decimal numbers to hundredths. Know the fraction and decimal equivalents for halves and fourths (e.g., 1/2 = 0.5 = 0.50, 7/4 = 1 3/4 = 1.75). Students will:

• Use operations to solve problems using distances • Use correct operations to solve intervals of time • Use correct operations to solve problems about volume • Use correct operations to solve problems about masses of objects • Use correct operations to solve problems about money • Use place value to round numbers to any given place • Write tenths in decimal and fraction form • Write hundredths in decimal and fraction form • Use models to represent decimal numbers • Use standard form to represent decimal numbers • Use expanded form to represent decimal numbers • Understand fraction and decimal equivalents


Addition Decimal decimal Denominator Difference Equations Expanded form Fluently Fractions Hundredths Mass Models Notation Numerator Represent Standard form Subtraction Sum Symbols Tenths Unknown number Volume Whole numbers

Week 5:


Activities

Vocabulary

Standards: 4.C.4: Multiply fluently within 100. 4.G.3: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint. 4.AT.1: Solve real-world problems involving addition and subtraction of multi-digit whole numbers (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). 4.NS.3: Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers. Name and write mixed numbers using objects or pictures. Name and write mixed numbers as improper fractions using objects or pictures. Students will:

• Recognize angles as geometric shapes • Recognize angles are formed by two rays that share a common endpoint • Solve problems using addition and subtraction • Express whole numbers as fractions • Recognize fractions that are equivalent to whole numbers • Name mixed numbers using objects or pictures • Write mixed numbers using objects or pictures • Name mixed numbers as improper fractions • Write mixed numbers as improper fractions

AIMS Internet Resources:

Angles Common Denominator Endpoint Equations Equivalent Express Fraction Geometric shape Improper fraction Mixed numbers Numerator Ray Represent Symbol Unknown number Whole numbers

Week 6:


Activities

Vocabulary

Standards: 4.C.4: Multiply fluently within 100. 4.AT.1: Solve real-world problems involving addition and subtraction of multi-digit whole numbers (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). 4.C.2: Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Describe the strategy and explain the reasoning. 4.C.7: Show how the order in which two numbers are multiplied (commutative property) and how numbers are grouped in multiplication (associative property) will not change the product. Use these properties to show that numbers can by multiplied in any order. Understand and use the distributive property. 4.C.1: Add and subtract multi-digit whole numbers fluently using a standard algorithmic approach. Students will:

• Solve addition and subtraction problems • Multiply whole numbers using strategies based on place value • Use the commutative property • Use the associative property • Use the distributive property • Add and subtract whole numbers fluently


Addition Algorithmic approach Associative property Commutative property Difference Distributive property Equation Factors Fluently Operation Place value Product Reasoning Represent Strategy Subtraction Sum Symbol Unknown number Variable Whole number

https://www.google.com/imgres?imgurl=http://ecx.images-amazon.com/images/I/81YunmpkRHL._SX466_.jpg&imgrefurl=http://www.amazon.com/Basic-Properties-Numbers-Educational-Classroom/dp/B005QQ4U9K&h=314&w=466&tbnid=XPgQ5Hdn94zN9M:&docid=fxZ5jIfceFP4FM&ei=YFnpVorkIIf8jgSK2oDAAw&tbm=isch&ved=0ahUKEwiKlKWAosXLAhUHvoMKHQotADgQMwhWKDEwMQ

Weeks 7-9:



solving them.

PS.1

Reason


PS.2



others PS.3

Model with

Mathematics

PS.4

Use appropriate

tools strategically

PS.5

Attend to precision

PS.6


structure

PS. 7

Look for and


PS.8





estimate


conclusions, assess




Week 7:


Activities

Vocabulary

Standards: 4.C.4: Multiply fluently within 100. 4.NS.1: Read and write whole numbers up to 1,000,000. Use words, models, standard form and expanded form to represent and show equivalent forms of whole numbers up to 1,000,000. 4.NS.3: Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers. Name and write mixed numbers using objects or pictures. Name and write mixed numbers as improper fractions using objects or pictures. 4.M.3: Use the four operations (addition, subtraction, multiplication and division) to solve real-world problems involving distances, intervals of time, volumes, masses of objects, and money. Include addition and subtraction problems involving simple fractions and problems that require expressing measurements given in a larger unit in terms of a smaller unit. 4.M.1: Measure length to the nearest quarter-inch, eighth-inch, and millimeter. Students will:

• Read whole numbers up to 1,000,000 • Write whole numbers up to 1,000,000 • Use words to represent numbers to 1,000,000 • Use models to represent numbers to 1,000,000 • Use standard form to represent numbers to 1,000,000 • Use expanded form to represent numbers to 1,000,000 • Show equivalent forms of whole numbers to 1,000,000 • Understand whole numbers as fractions • Recognize equivalent fractions to whole numbers • Name mixed numbers using objects or pictures • Write mixed numbers using objects or pictures • Measure length to the nearest quarter-inch • Measure length to the nearest eight-inch • Measure length to the nearest millimeter • Use four operations involving distances • Use four operations involving intervals of time • Use four operations involving masses of objects • Use four operations involving money


Denominator Eighth-inch Equivalent Expanded form Fluently Fraction Improper fractions Length Mass Measurement Millimeter Mixed numbers Models Models Numerator Quarter-inch Represent Standard form Volume Whole numbers Word form

Week 8:


Activities

Vocabulary

Standards: 4.C.4: Multiply fluently within 100. 4.C.1: Add and subtract multi-digit whole numbers fluently using a standard algorithmic approach. 4.AT.4: Solve real-world problems with whole numbers involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem), distinguishing multiplicative comparison from additive comparison. [In grade 4, division problems should not include a remainder.] 4.M.3: Use the four operations (addition, subtraction, multiplication and division) to solve real-world problems involving distances, intervals of time, volumes, masses of objects, and money. Include addition and subtraction problems involving simple fractions and problems that require expressing measurements given in a larger unit in terms of a smaller unit. 4.C.2: Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Describe the strategy and explain the reasoning. Students will:

• Add and subtract fluently • Solve real world problems with whole numbers • Use multiplicative comparison using drawings and equations • Represent an unknown number with a symbol • Distinguish between multiplicative and additive comparison • Use four operations involving distances • Use four operations involving intervals of time • Use four operations involving volume • Use four operations involving masses of objects • Use four operations involving money • Solve addition and subtract problems involving simple fractions • Solve add and subtract problems expressing measurements given in a larger unit in

terms of a smaller unit • Multiply a whole number • Use strategies when multiplying based on place value • Use properties of operations • Describe strategy used when multiplying • Explain reasoning when multiplying


Addition Algorithmic approach Denominator Difference Equations Factor Fluently Fraction Mass Multiplicative comparison Numerator Product Reasoning Represent Strategy Subtraction Sum Symbol Unknown number Variable Volume

Week 9:


Activities

Vocabulary

Standards: 4.C.4: Multiply fluently within 100. 4.C.1: Add and subtract multi-digit whole numbers fluently using a standard algorithmic approach. 4.C.2: Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Describe the strategy and explain the reasoning. 4.C.7: Show how the order in which two numbers are multiplied (commutative property) and how numbers are grouped in multiplication (associative property) will not change the product. Use these properties to show that numbers can by multiplied in any order. Understand and use the distributive property. 4.NS.8: Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. 4.AT.2: Recognize and apply the relationships between addition and multiplication, between subtraction and division, and the inverse relationship between multiplication and division to solve real-world and other mathematical problems. 4.AT.4: Solve real-world problems with whole numbers involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem), distinguishing multiplicative comparison from additive comparison. [In grade 4, division problems should not include a remainder.] 4.C.3: Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Describe the strategy and explain the reasoning. Students will:

• Add and subtract fluently • Multiply whole numbers based on place value • Multiply whole numbers based on the properties of operations • Describe strategy with multiplying whole numbers • Explain reasoning when multiplying whole numbers • Understand commutative property • Understand associative property • Understand distributive property • Find all factor pairs for whole numbers (include 2 numbers) • Recognize relationships between addition and multiplication • Recognize relationships between subtraction and division • Apply relationships between addition and multiplication • Apply relationships between subtraction and division • Solve problems involving multiplicative comparison • Solve problems using a symbol to represent an unknown number • Find whole number quotients based on place value • Find whole number quotients with remainders based on place value


Additive comparison Algorithmic approach Associative property Commutative property Distributive property Factor Factor pairs Fluently Inverse Inverse operation Multiplicative comparison Place value Product Properties Quotient Whole number

Weeks 10-12:



solving them.

PS.1

Reason


PS.2



others PS.3

Model with

Mathematics

PS.4

Use appropriate

tools strategically

PS.5

Attend to precision

PS.6


structure

PS. 7

Look for and


PS.8





estimate


conclusions, assess




Week 10:


Activities

Vocabulary

Standards: 4.C.4: Multiply fluently within 100. 4.NS.9: Use place value understanding to round multi-digit whole numbers to any given place value. 4.NS.8: Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. 4.C.2: Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Describe the strategy and explain the reasoning. Students will:

• Use place value to round numbers • Find all factor pairs for whole numbers • Find all factor pairs for two numbers • Multiply a whole number up to four digits by one digit whole number • Multiply two two-digit numbers using strategies based on place value • Multiply two two-digit numbers using properties of operations • Describe the strategy used for multiplication • Describe the reasoning used for multiplication


Algorithmic approach Estimate Factor Factor pairs Fluently Multiple Operation Place value Product Quotient Range Reasoning Round Strategy Whole number

Week 11:


Activities

Vocabulary

Standards: 4.C.4: Multiply fluently within 100. 4.AT.5: Solve real-world problems involving addition and subtraction of fractions referring to the same whole and having common denominators (e.g., by using visual fraction models and equations to represent the problem). 4.AT.4: Solve real-world problems with whole numbers involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem), distinguishing multiplicative comparison from additive comparison. [In grade 4, division problems should not include a remainder.] Students will:

• Solve problems involving addition and subtraction of fractions • Understand fractions having same whole and common denominators • Use visual fraction models to represent addition and subtraction of fractions • Use equations to represent addition and subtraction of fractions • Solve problems using multiplicative comparison • Distinguish multiplicative comparison from additive comparison • Use drawing to represent equations with an unknown number • Use a symbol to represent equations with an unknown number


Additive comparison Algorithmic approach Denominator Dividend Division Divisor Equations Fluently Fraction Model Multiplicative comparison Numerator Quotient Represent Visual fraction Whole number

Week 12:


Activities

Vocabulary

Standards: 4.C.4: Multiply fluently within 100. 4.C.2: Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Describe the strategy and explain the reasoning. 4.G.1: Identify, describe, and draw parallelograms, rhombuses, and trapezoids using appropriate tools (e.g., ruler, straightedge and technology). 4.G.5: Classify triangles and quadrilaterals based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles (right, acute, obtuse). 4.C.3: Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Describe the strategy and explain the reasoning. Students will:

• Multiply a whole number up to four digits • Use strategies based on place value • Use properties of operations • Describe strategy used in multiplication • Explain reasoning used in multiplication • Identify parallelogram, rhombus, and trapezoid • Describe parallelogram, rhombus, and trapezoid • Draw parallelogram, rhombus, and trapezoid • Use tools appropriately • Classify triangles and quadrilaterals based on types of lines • Classify parallel and perpendicular lines • Understand types of angles • Find whole number quotients • Find whole number quotients with remainders • Use strategies based on place value • Use strategies based on properties of operations • Understand the relationship between multiplication and division • Describe the strategy used with multiplying or dividing • Explain reasoning used for multiplying and dividing


Algorithmic approach Classify Dividend Divisor Factor Fluently Multiply Parallelogram Place value Product Quadrilateral Quotient Reasoning Remainders Rhombus Ruler Straightedge Tools Trapezoid Triangle Whole number

Weeks 13-15:



solving them.

PS.1

Reason


PS.2



others PS.3

Model with

Mathematics

PS.4

Use appropriate

tools strategically

PS.5

Attend to precision

PS.6


structure

PS. 7

Look for and


PS.8





estimate


conclusions, assess




Week 13:


Activities

Vocabulary

Standards: 4.C.4: Multiply fluently within 100. 4.M.1: Measure length to the nearest quarter-inch, eighth-inch, and millimeter. 4.C.3: Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Describe the strategy and explain the reasoning. 4.AT.5: Solve real-world problems involving addition and subtraction of fractions referring to the same whole and having common denominators (e.g., by using visual fraction models and equations to represent the problem). Students will:

• Measure length to the nearest quarter-inch • Measure length to the nearest eighth-inch • Measure length to the nearest millimeter • Find whole number quotients • Find whole number quotients with remainders • Use strategies based on place value • Use properties of operations • Understand relationship between multiplication and division • Describe strategy with multiplying or dividing • Explain reasoning for multiplying or dividing


Algorithmic approach Denominator Dividend Divisor Eighth-inch Equations Fluently Fraction Length Measure Millimeter Model Numerator Place value Properties Quarter-inch Quotient Reasoning Remainders Represent Strategy Whole numbers

Week 14:


Activities

Vocabulary

Standards: 4.C.4: Multiply fluently within 100. 4.G.5: Classify triangles and quadrilaterals based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles (right, acute, obtuse). 4.G.2: Recognize and draw lines of symmetry in two-dimensional figures. Identify figures that have lines of symmetry. Students will:

• Classify triangles and quadrilaterals based on types of lines • Classify triangles and quadrilaterals based on angles • Identify parallel lines • Identify perpendicular lines • Recognize lines of symmetry in two-dimensional figures • Draw lines of symmetry in two-dimensional figures • Identify figures that have lines of symmetry


Acute Algorithmic approach Angles Fluently Obtuse Parallel Parallel Lines Perpendicular lines Quadrilateral Right Symmetry Triangle Two-dimensional

Week 15:


Activities

Vocabulary

Standards: 4.C.4: Multiply fluently within 100. 4.DA.1: Formulate questions that can be addressed with data. Use observations, surveys, and experiments to collect, represent, and interpret the data using tables (including frequency tables), line plots, and bar graph 4.G.4: Identify, describe, and draw rays, angles (right, acute, obtuse), and perpendicular and parallel lines using appropriate tools (e.g., ruler, straightedge and technology). Identify these in two-dimensional figures. 4.M.5: Understand that an angle is measured with reference to a circle, with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. Understand an angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure other angles. Understand an angle that turns through n one-degree angles is said to have an angle measure of n degrees. 4.C.3: Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Describe the strategy and explain the reasoning. 4.AT.5: Solve real-world problems involving addition and subtraction of fractions referring to the same whole and having common denominators (e.g., by using visual fraction models and equations to represent the problem). Students will:

• Formulate questions regarding data • Use various methods to represent data • Interpret data using tables • Understand frequency tables, line plots, and bar graphs • Identify rays and angles • Describe rays and angles • Draw rays and angles • Identify perpendicular and parallel lines • Use appropriate tools • Identify angles and lines in two-dimensional figures • Understand how to measure an angle with a protractor • Find whole number quotients • Find whole number quotients with remainders • Use strategies based on place value • Understand relationship between multiplication and division • Describe strategy used when multiplying and dividing • Explain the reasoning with multiplying and dividing • Solve problems involving addition and subtraction of fractions • Use visual fraction models to represent the problem • Use equations to represent the problem


Algorithmic approach Angles Circle Data Denominator Dividend Divisor Endpoint Experiments Fluently Fraction Numerator Observations Parallel lines Perpendicular lines Place value Quotient Ray Remainders Represent Strategy Surveys Tables Tools Whole number

Weeks 16-18:



solving them.

PS.1

Reason


PS.2



others PS.3

Model with

Mathematics

PS.4

Use appropriate

tools strategically

PS.5

Attend to precision

PS.6


structure

PS. 7

Look for and


PS.8





estimate


conclusions, assess




Week 16:


Activities

Vocabulary

Standards: 4.C.4: Multiply fluently within 100. 4.NS.9: Use place value understanding to round multi-digit whole numbers to any given place value. 4.C.2: Multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Describe the strategy and explain the reasoning. Students will:

• Use place value to round numbers • Multiply whole numbers • Use strategies to multiply whole numbers based on place value • Use strategies to multiply whole numbers based on properties of operations • Describe strategy used when multiplying • Explain reasoning when multiplying


Algorithmic approach Estimate Factors Fluently Operations Place value Product Reasoning Round Strategy Whole number

Week 17:


Activities

Vocabulary

Standards: 4.C.4: Multiply fluently within 100. 4.NS.3: Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers. Name and write mixed numbers using objects or pictures. Name and write mixed numbers as improper fractions using objects or pictures. 4.C.3: Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Describe the strategy and explain the reasoning. 4.NS.7: Compare two decimals to hundredths by reasoning about their size based on the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions (e.g., by using a visual model). Students will:

• Express whole numbers as fractions • Recognize fractions as equivalent whole numbers • Name mixed numbers using objects or pictures • Write mixed numbers using objects or pictures • Find whole number quotients using strategies based on place value • Find whole number quotients with remainders using strategies based on place value • Understand the relationship between multiplication and division • Describe the strategy for multiplication • Explain the reasoning for multiplication • Compare two decimals to hundredths • Reason about size of decimal based on same whole when comparing • Record results of comparison • Justify conclusions of comparing • Use a visual model when comparing


Algorithmic approach Compare Decimals Dividend Divisor Equal to Equivalent Fluently Fraction Greater than Hundredth Improper fraction Less than Mixed numbers Place value Properties Quotient Reasoning Remainder Strategy Tenth Whole numbers

Week 18:


Activities

Vocabulary

Standards: 4.C.4: Multiply fluently within 100. 4.G.1: Identify, describe, and draw parallelograms, rhombuses, and trapezoids using appropriate tools (e.g., ruler, straightedge and technology). 4.G.5: Classify triangles and quadrilaterals based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles (right, acute, obtuse). 4.NS.6: Write tenths and hundredths in decimal and fraction notations. Use words, models, standard form and expanded form to represent decimal numbers to hundredths. Know the fraction and decimal equivalents for halves and fourths (e.g., 1/2 = 0.5 = 0.50, 7/4 = 1 3/4 = 1.75). Students will:

• Identify parallelograms, rhombuses, and trapezoids • Describe parallelograms, rhombuses, and trapezoids • Draw parallelograms, rhombuses, and trapezoids • Use appropriate tools to draw two dimensional shapes • Classify triangles based on types of lines and angles • Classify quadrilaterals based on types of lines and angles • Identify parallel lines • Identify perpendicular lines • Write decimal forms in fraction notations • Use words for standard form to represent a decimal to hundredths • Use models for standard form to represent a decimal to hundredths • Use expanded form to represent a decimal to hundredths • Know fraction and decimal equivalents


Algorithmic approach Decimal Equivalent Expanded form Fluently Fraction Hundredth Model Notation Parallel Parallel lines Parallelogram Perpendicular Perpendicular lines Quadrilateral Rhombus Ruler Standard form Straightedge Tenth Tools Trapezoid Triangle

Weeks 19-21:



solving them.

PS.1

Reason


PS.2



others PS.3

Model with

Mathematics

PS.4

Use appropriate

tools strategically

PS.5

Attend to precision

PS.6


structure

PS. 7

Look for and


PS.8





estimate


conclusions, assess




Week 19:


Activities

Vocabulary

Standards: 4.C.4: Multiply fluently within 100. 4.DA.1: Formulate questions that can be addressed with data. Use observations, surveys, and experiments to collect, represent, and interpret the data using tables (including frequency tables), line plots, and bar graphs. 4.NS.6: Write tenths and hundredths in decimal and fraction notations. Use words, models, standard form and expanded form to represent decimal numbers to hundredths. Know the fraction and decimal equivalents for halves and fourths (e.g., 1/2 = 0.5 = 0.50, 7/4 = 1 3/4 = 1.75). 4.NS.5: Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark, such as 0, 1/2, and 1). Recognize comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions (e.g., by using a visual fraction model). Students will:

• Formulate questions about data • Use various methods to represent data • Interpret data using different types of tables • Write tenths and hundredths in decimal notations • Write tenths and hundredths if fraction notations • Use words for standard form to represent a decimal number • Use models for standard form to represent a decimal number • Use words for expanded form to represent a decimal number • Understand fraction equivalents • Compare two fractions • Understand how to use benchmark fractions • Recognize comparisons when referring to the same whole • Record results using appropriate symbol • Justify conclusions with appropriate symbol • Use visual fraction model to represent conclusions


Algorithmic approach Bar graphs Benchmark fraction Circle Graph Conclusion Data Data set Decimal Denominator Equivalent Expanded form Fluently Fraction Frequency Frequency tables Greater than Hundredths Justify Less than Line plots Models Numerator Represent Standard form Symbol Tenths

Week 20:


Activities

Vocabulary

Standards: 4.C.4: Multiply fluently within 100. 4.DA.1: Formulate questions that can be addressed with data. Use observations, surveys, and experiments to collect, represent, and interpret the data using tables (including frequency tables), line plots, and bar graphs. 4.NS.3: Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers. Name and write mixed numbers using objects or pictures. Name and write mixed numbers as improper fractions using objects or pictures. 4.C.5: Add and subtract fractions with common denominators. Decompose a fraction into a sum of fractions with common denominators. Understand addition and subtraction of fractions as combining and separating parts referring to the same whole. 4.C.3: Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Describe the strategy and explain the reasoning. 4.M.4: Apply the area and perimeter formulas for rectangles to solve real-world problems and other mathematical problems. Recognize area as additive and find the area of complex shapes composed of rectangles by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts; apply this technique to solve real-world problems and other mathematical problems. Students will:

• Formulate questions about data • Use various methods to represent data • Interpret data using different types of tables • Express whole numbers as fractions • Recognize fractions are equivalent to whole numbers • Name mixed numbers using objects or pictures • Write mixed numbers using objects or pictures • Name mixed numbers as improper fractions • Write mixed numbers as improper fractions • Add fractions with common denominators • Subtract fractions with common denominators • Decompose a fraction • Understand addition of fractions as combining parts referring to same whole • Understand subtraction of fractions as separating parts referring to same whole • Apply area formulas • Apply perimeter formulas • Find whole number quotients • Find whole number quotients with remainders • Describe strategy used with multiplying •

****ADD STANDARDS!!!


Algorithmic approach Area Complex shapes Data Decompose Decompose a fraction Decomposing Denominator Dividend Divisors Equivalent Fluently Fraction Frequency table Improper fraction Interpret Mixed numbers Numerator Perimeter Place value Quotient Represent Sum Tables

Week 21:


Activities

Vocabulary

Standards: 4.C.4: Multiply fluently within 100. 4.NS.4: Explain why a fraction, a/b, is equivalent to a fraction, (n × a)/(n × b), by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. [In grade 4, limit denominators of fractions to 2, 3, 4, 5, 6, 8, 10, 25, 100.] 4.AT.1: Solve real-world problems involving addition and subtraction of multi-digit whole numbers (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). 4.AT.4: Solve real-world problems with whole numbers involving multiplicative comparison (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem), distinguishing multiplicative comparison from additive comparison. [In grade 4, division problems should not include a remainder.] 4.C.7: Show how the order in which two numbers are multiplied (commutative property) and how numbers are grouped in multiplication (associative property) will not change the product. Use these properties to show that numbers can by multiplied in any order. Understand and use the distributive property. Students will:

• Explain why a fraction is equivalent to another fraction • Use visual fraction models to show equivalency • Understand denominators represent the size of the whole • Solve problems involving addition of multi-digit numbers • Solve problems involving subtraction of multi-digit numbers • Use drawings to represent unknown numbers • Use symbols to represent unknown numbers • Solve problems with whole numbers involving multiplicative comparison • Distinguish between multiplicative and additive comparison • Show the order in which two numbers are multiplied • Understand the commutative property • Understand the associative property • Understand the distributive property


Algorithmic approach Associative property Commutative property Denominator Distributive property Drawing Equivalent Fluently Fraction Model Numerator Symbol Unknown number Visual Whole number

Weeks 22-24:



solving them.

PS.1

Reason


PS.2



others PS.3

Model with

Mathematics

PS.4

Use appropriate

tools strategically

PS.5

Attend to precision

PS.6


structure

PS. 7

Look for and


PS.8





estimate


conclusions, assess




Week 22:


Activities

Vocabulary

Standards: 4.C.4: Multiply fluently within 100. 4.C.3: Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Describe the strategy and explain the reasoning. 4.NS.4: Explain why a fraction, a/b, is equivalent to a fraction, (n × a)/(n × b), by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. [In grade 4, limit denominators of fractions to 2, 3, 4, 5, 6, 8, 10, 25, 100.] 4.NS.9: Use place value understanding to round multi-digit whole numbers to any given place value. Students will:

• Find whole number quotients • Find whole number quotients with remainders • Use strategies based on place value • Use properties of operations • Understand the relationship between multiplication and division • Describe the strategy of multiplying or dividing • Explain the reasoning of multiplying or dividing • Explain why a fraction is equivalent to another fraction • Use visual fraction models to show equivalency • Recognize equivalent fractions • Use place value to round numbers • Use place value to estimate numbers


Algorithmic approach Denominator Dividend Divisor Equivalent Estimate Fluently Fraction Numerator Place value Quotient Reasoning Remainder Round Strategy Whole number

Week 23:


Activities

Vocabulary

Standards: 4.C.4: Multiply fluently within 100. 4.NS.4: Explain why a fraction, a/b, is equivalent to a fraction, (n × a)/(n × b), by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. [In grade 4, limit denominators of fractions to 2, 3, 4, 5, 6, 8, 10, 25, 100.] 4.NS.5: Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators, or by comparing to a benchmark, such as 0, 1/2, and 1). Recognize comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions (e.g., by using a visual fraction model). 4.NS.6: Write tenths and hundredths in decimal and fraction notations. Use words, models, standard form and expanded form to represent decimal numbers to hundredths. Know the fraction and decimal equivalents for halves and fourths (e.g., 1/2 = 0.5 = 0.50, 7/4 = 1 3/4 = 1.75). 4.C.3: Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Describe the strategy and explain the reasoning. Students will:

• Explain why a fraction is equivalent to another fraction • Use visual fraction models to show equivalency • Recognize equivalent fractions • Compare two fractions • Understand how to use a benchmark fraction or number • Recognize comparisons of fractions represent the same whole • Record results of comparisons using correct symbol • Write tenths in decimal notations • Write hundredths in fraction notations • Use words in standard form • Use words in expanded form to represent a decimal to hundredths • Use models in standard form to represent a decimal to hundredths • Understand fraction and decimal equivalents • Find whole number quotients • Find whole number quotients with remainders • Use strategies based on place value with dividing • Use properties of operations when dividing • Understand the relationship between multiplication and division • Describe strategy used when multiplying and dividing • Explain the reasoning used when multiplying and dividing


Algorithmic approach Denominator Fluently Fraction Numerator Place value Quotient

Week 24:


Activities

Vocabulary

Standards: 4.C.4: Multiply fluently within 100. 4.C.5: Add and subtract fractions with common denominators. Decompose a fraction into a sum of fractions with common denominators. Understand addition and subtraction of fractions as combining and separating parts referring to the same whole. 4.C.6: Add and subtract mixed numbers with common denominators (e.g. by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction). 4.DA.2: Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using data displayed in line plots. 4.DA.1: Formulate questions that can be addressed with data. Use observations, surveys, and experiments to collect, represent, and interpret the data using tables (including frequency tables), line plots, and bar graphs. Students will:

• Add and subtract fractions with common denominators • Decompose a fraction into a sum of fractions • Understand addition of fractions is combining parts • Understand subtraction of fractions is separating parts • Add and subtract mixed numbers with common denominators • Make a line plot to display data set of measurements in fractional units • Solve problems involving addition and subtraction of fractions • Use data displayed in line plots • Formulate questions about data • Use various methods to represent data • Use various methods to interpret data using tables, line plots, and bar graphs


Algorithmic approach Combining Data set Decompose a fraction Denominator Display Equivalent Equivalent fraction Fluently Fraction Frequency Frequency table Interpret Line plot Measurement Mixed numbers Numerator Operations Properties Separating Sum

Weeks 25-27:



solving them.

PS.1

Reason


PS.2



others PS.3

Model with

Mathematics

PS.4

Use appropriate

tools strategically

PS.5

Attend to precision

PS.6


structure

PS. 7

Look for and


PS.8





estimate


conclusions, assess




Week 25:


Activities

Vocabulary

Standards: 4.C.4: Multiply fluently within 100. 4.M.6: Measure angles in whole-number degrees using appropriate tools. Sketch angles of specified measure. 4.M.4: Apply the area and perimeter formulas for rectangles to solve real-world problems and other mathematical problems. Recognize area as additive and find the area of complex shapes composed of rectangles by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts; apply this technique to solve real-world problems and other mathematical problems. Students will:

• Measure angles using a protractor • Apply area formulas to solve real-world problems • Apply perimeter formulas to solve real-world problems • Understand area as an additive • Find area of complex shapes composed of rectangles • Decompose shapes into non-overlapping rectangles to find area of complex shapes • Solve real-world problems using this technique


Additive Algorithmic approach Angles Area Complex shapes Composed Decompose Fluently Measure Perimeter Protractor Tools

Week 26:


Activities

Vocabulary

Standards: 4.C.4: Multiply fluently within 100. Students will:


Fluently Algorithmic approach

Week 27:


Activities

Vocabulary



Weeks 28-30:



solving them.

PS.1

Reason


PS.2



others PS.3

Model with

Mathematics

PS.4

Use appropriate

tools strategically

PS.5

Attend to precision

PS.6


structure

PS. 7

Look for and


PS.8





estimate


conclusions, assess




Week 28:


Activities

Vocabulary



Week 29:


Activities

Vocabulary



Week 30:


Activities

Vocabulary



Weeks 31-33:



solving them.

PS.1

Reason


PS.2



others PS.3

Model with

Mathematics

PS.4

Use appropriate

tools strategically

PS.5

Attend to precision

PS.6


structure

PS. 7

Look for and


PS.8





estimate


conclusions, assess




Week 31:


Activities

Vocabulary



Week 32:


Activities

Vocabulary



Week 33:


Activities

Vocabulary



Weeks 34-36:



solving them.

PS.1

Reason


PS.2



others PS.3

Model with

Mathematics

PS.4

Use appropriate

tools strategically

PS.5

Attend to precision

PS.6


structure

PS. 7

Look for and


PS.8





estimate


conclusions, assess




Week 34:


Activities

Vocabulary



Week 35:


Activities

Vocabulary



Week 36:


Activities

Vocabulary




Activities

Vocabulary

Standards: Students will:


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