6th grade curriculum guide 2012-2013 Time Frame:...

6th grade curriculum guide 2012-2013

1 Power Standards in green Complementary Standards in yellow

Connected Math Unit: Bits and Pieces I Following is a general outline of the 1st unit for Grade 6. In this unit the focus is on multiplying and dividing fractions and decimals. Students

solve a wide variety of problems that involve the numbers they see every day- whole numbers, fractions and decimals. By using approximations of fractions and decimals, students estimate computations and verify that their answers make sense.

Standards Assessment/ Student Evidence

Academic Vocabulary

Resources

6.1 Core Content: Multiplication and division of fractions and decimals (Numbers, Operations, Algebra) Link to OSPI Explanatory Comments and Examples 6.1.A Compare and order non-negative fractions, decimals, and integers using the number line, lists, and the symbols <, >, or =.

Sample tasks may look like this: Sharon ran of a mile. Then

she walked of mile. Which expression correctly explains the relationship between the two distances?

A. >

B. <

C. =

D. <

Benchmark Common denominator Denominator Improper fractions Mixed number Numerator Unit fraction

Connected Mathematics Unit Bits & Pieces I

AND Scott Foresman-Addison Wesley textbook

AND Math on Call Resource Book

6.3 Core Content: Ratios, rates, and percents Link to OSPI Explantory Comments and Examples

6.3.C Represent percents visually and numerically, and convert between the fractional, decimal, and percent representations of a number.

Sample tasks may look like this: Jack recently took a spelling test that had twenty-five words. He correctly spelled 20 words. What percentage of the words did he spell correctly?

Percent Equivalent fractions Ratio Rational number

Time Frame: September

Trimester 1

http://www.k12.wa.us/Mathematics/Standards/WAMathStandardsGradesK-8.pdf#Page=82

http://www.mathematicsdictionary.com/english/vmd/full/b/benchmarknumber.htm

http://www.mathsisfun.com/definitions/common-denominator.html

http://www.mathsisfun.com/definitions/denominator.html

http://www.mathsisfun.com/definitions/improper-fraction.html

http://www.mathsisfun.com/mixed-fractions.html

http://www.mathsisfun.com/definitions/numerator.html

http://www.mathsisfun.com/definitions/unit-fraction.html


http://www.mathsisfun.com/definitions/percent.html

http://www.mathsisfun.com/definitions/equivalent-fractions.html

http://www.mathsisfun.com/definitions/ratio.html

http://www.mathsisfun.com/definitions/rational-number.html



Connected Math: Bits and Pieces II Following is a general outline of the 2nd unit for Grade 6. In this unit, the focus is on representing multiplication and division of non-negative fractions and decimals using the area model and the number line, and connecting each representation to the related equation. Students use

strategies for mental computations with non-negative whole numbers, fractions and decimals. Standards Assessment/

Student Evidence Academic

Vocabulary Resources

6.1 Core Content: Multiplication and division of fractions and decimals (Numbers, Operations, Algebra) Link to OSPI Explanatory Comments and Examples 6.1.B Represent multiplication and division of non-negative fractions and decimals using area models and the number line, and connect each representation to the related equation.

Sample tasks may look like this: Joe cut his string into four pieces. The pieces were each 2 ½ feet long, how long was the piece of string before he cut it?

Denominator Equivalent fractions Numerator Unit fraction

Connected Mathematics Unit Bits & Pieces II AND Contexts for Learning Minilessons for Operations with Fractions, Decimals and Percents

6.1.C Estimate products and quotients of fractions and decimals.

Sample tasks may look like this: Larry has of a licorice rope. He ate of the licorice rope. Estimate the amount of

the licorice rope that Larry ate.

Benchmark

Time Frame: October

Trimester 1


http://www.mathsisfun.com/definitions/denominator.html

http://www.mathsisfun.com/definitions/equivalent-fractions.html

http://www.mathsisfun.com/definitions/numerator.html

http://www.mathsisfun.com/definitions/unit-fraction.html

http://www.mathematicsdictionary.com/english/vmd/full/b/benchmarknumber.htm




Academic Vocabulary

Resources

6.1 Core Content: Multiplication and division of fractions and decimals (Numbers, Operations, Algebra) Link to OSPI Explanatory Comments and Examples 6.1.D Fluently and accurately multiply and divide non-negative fractions and explain the inverse relationship between multiplication and division with fractions

Sample tasks may look like this: Solve.

divided by 4

Inverse relationship Fact family Reciprocal Algorithm


6.1.H Solve single- and multi-step word problems involving operations with fractions and decimals and verify the solutions.

Sample tasks may look like this: Eight boys have 4 donuts which they share equally among themselves. How much of a donut will each person receive if they share them equally?


http://www.mathsisfun.com/definitions/inverse.html

http://www.bellaonline.com/articles/art57615.asp

http://www.mathsisfun.com/definitions/reciprocal.html

http://www.mff.org/mmc/div_fractions.pdf



Standards Assessment/



6.5. Additional Key Content (Numbers, Operations) Link to OSPI Explanatory Comments and Examples 6.5.A Use strategies for mental computations with non-negative whole numbers, fractions, and decimals.

Sample tasks may look like this: Examples: • John wants to find the total number of hours he worked this week. Use his time card below to find the total.

Days Mon Tues Wed Thurs Fri Days 4 3 6 7 1

• What is the total cost for items priced at $25.99 and $32.95? (A student may think of something like 25.99 + 32.95 = (26 + 33) – 0.06 = 58.94.)





Investigation Unit: Containers and Cubes

Following is a general outline of the 3rd unit for Grade 6. In this unit, the focus is on two- and three-dimensional figures. Students extend what they know about area and perimeter to more complex two-dimensional figures, including circles. They find the surface area and volume of

simple three-dimensional figures. As they learn these procedures, students can solve problems involving more complex figures than in earlier grades and use geometry to deal with a wider range of situations.




6.4. Core Content: Two- and three-dimensional figures (Geometry/Measurement, Algebra) Link to OSPI Explanatory Comments and Examples 6.4.D Recognize and draw two-dimensional representations of three-dimensional figures.

Sample tasks may look like this: The net of a cylinder consists of two circles and a rectangle. Example:

Net

Investigations Unit: Containers and Cubes AND Scott Foresman-Addison Wesley AND Math at Hand Math on Call

Time Frame: November

Trimester 1

http://www.k12.wa.us/Mathematics/Standards/WAMathStandardsGradesK-8.pdf

http://www.mathsisfun.com/definitions/net.html






6.4. Core Content: Two- and three-dimensional figures (Geometry/Measurement, Algebra) Link to OSPI Explantory Comments and Examples 6.4.E Determine the surface area and volume of rectangular prisms using appropriate formulas and explain why the formulas work.

Sample tasks may look like this: You have a box with the dimensions of 5 units X 6 units X 3 units. What is the surface area?

Volume Surface area Cubic measure Prism Cube Square Measure

Investigations Unit: Containers and Cubes

AND Scott Foresman-Addison Wesley

AND Math at Hand Math on Call 6.4.F

Determine the surface area of a pyramid.

Sample tasks may look like this: A building designer is painting a monument that is in the shape of a pyramid. The base is a square 4 units on a side. Each face is a triangle with base 4 and height 7. What is the surface area of the pyramid?

Pyramid


http://www.mathsisfun.com/definitions/volume.html

http://www.mathsisfun.com/definitions/surface-area.html

http://www.mathsisfun.com/definitions/cubic-measure.html

http://www.mathsisfun.com/definitions/prism.html

http://www.mathsisfun.com/definitions/cube.html

http://www.mathsisfun.com/definitions/square-measure.html

http://www.mathsisfun.com/definitions/pyramid.html




Academic Vocabulary

Resources

6.4. Core Content: Two- and three-dimensional figures (Geometry/Measurement, Algebra) Link to OSPI Explantory Comments and Examples 6.4.G Describe and sort polyhedra by their attributes: parallel faces, types of faces, number of faces, edges, and vertices.

Sample tasks may look like this: Prisms and pyramids are the focus at this level. Examples: How many pairs of parallel faces does each polyhedron have? Explain your answer.

Attribute Polyhedron Parallel faces Edge Face

Investigations Unit: Containers and Cubes

AND Scott Foresman-Addison Wesley

AND Math at Hand Math on Call

Time Frame: December - February

Trimester 2


http://www.mathsisfun.com/definitions/attribute.html

http://www.mathsisfun.com/definitions/polyhedron.html

http://www.mathsisfun.com/definitions/edge.html

http://www.mathsisfun.com/definitions/face.html



Connected Math Unit: Bits and Pieces III Following is a general outline of the 4th unit for Grade 6. In this unit, the focus is on providing experiences in building algorithms for the four

basic operations with decimals as well as opportunities for students to consider when such operations are useful in solving problems. Students develop and use benchmarks and other strategies to estimate the answers to computations with decimals.


Academic Vocabulary

Resources

6.1 Core Content: Multiplication and division of fractions and decimals (Numbers, Operations, Algebra) Link to OSPI Explanatory Comments and Examples 6.1.C Estimate products and quotients of fractions and decimals.

Sample tasks may look like this: MaryEllen went to Safeway to buy packs of pencils for her students. She bought:

• 23 packs of pencils that cost $1.25 each

What is the best estimate for the total amount of money MaryEllen spent?

Powers of 10

Connected Mathematics Unit Bits and Pieces III Contexts for Learning Minilessons for Operations with Fractions, Decimals and Percents

6.1.E Multiply and divide whole numbers and decimals by 1000, 100, 10, 1, 0.1, 0.01, and 0.001.

Sample tasks may look like this: Put these expressions in order from least to greatest: 5.1 x 1

5.1 x .001

5.1 x 100

5.1 x .01

Inverse relationship


http://www.mathsisfun.com/definitions/inverse-operation.html






6.1 Core Content: Multiplication and division of fractions and decimals (Numbers, Operations, Algebra) Link to OSPI Explanatory Comments and Examples 6.1.F Fluently and accurately multiply and divide non-negative decimals.

Sample tasks may look like this: Solve.

33 x 2.25 =

Repeating decimal Terminating decimal


6.1.G Describe the effect of multiplying or dividing a number by one, by zero, by a number between zero and one, and by a number greater than one.

Sample tasks may look like this: Without doing any computation, list 74, 0.43 × 74, and 74 ÷0.85 in increasing order and explain your reasoning. Explain why 4/0 is undefined.


http://www.mathsisfun.com/definitions/recurring-decimal.html

http://www.mathsisfun.com/definitions/terminating-decimal.html




Academic Vocabulary

Resources

6.1 Core Content: Multiplication and division of fractions and decimals (Numbers, Operations, Algebra) Link to OSPI Explanatory Comments and Examples 6.1.H Solve single- and multi-step word problems involving operations with fractions and decimals and verify the solutions.

Sample tasks may look like this: Betty bought 4.3 feet of string to make her kite. The cost was $0.90 per foot. What was the total cost of the string?


6.3 Core Content: Ratios, rates, and percents Link to OSPI Explantory Comments and Examples 6.3.C Represent percents visually and numerically, and convert between the fractional, decimal, and percent representations of a number.

Sample tasks may look like this: At Eleanor’s flower shop, 2 out of every 5 flowers Eleanor sells are roses. Which of the following represents the number of roses sold compared to the total number of flowers sold?

O A. 25% O B. 0.25 O C. 4% O D. 0.4






Academic Vocabulary

Resources


6.3.D Solve single- and multi-step word problems involving ratios, rates, and percents, and verify the solutions.

Sample tasks may look like this: Mary is buying a shirt at the clothing store. The shirt’s price is $30.00. Today’s special is 15% off all shirts. What is the cost of the shirt if she buys it today?


6.5. Additional Key Content (Numbers, Operations) Link to OSPI Explanatory Comments and Examples

6.5.A Use strategies for mental computations with non-negative whole numbers, fractions, and decimals.

Sample tasks may look like this: What is the total cost for items priced at $25.99 and $32.95? (A student may think of something like 25.99 + 32.95 = (26 + 33) – 0.06 = 58.94.)





Connected Math Unit: Covering and Surrounding Following is a general outline of the 5th unit for Grade 6. In this unit, the focus is on two-dimensional measurement. Students learn how to use the diameter to solve for the circumference of a circle. They will then extend this knowledge to determine the areas of circles. Students are also

expected to solve the area for various irregular figures.


Academic Vocabulary

Resources


6.3.E Identify the ratio of the circumference to the diameter of a circle as the constant π, and recognize 22/7 and 3.14 as common approximations of π.

Sample tasks may look like this: Luca’s bike tire has a circumference of 40 centimeters. Approximately what is the diameter of Luca’s bike tire?

Circle Pi

Connected Mathematics Unit Covering & Surrounding


AND Math on Call

6.4. Core Content: Two-and three-dimensional figures (Geometry/Measurement, Algebra) Link to OSPI Explanatory Comments and Examples 6.4.A Determine the circumference and area of circles.

Sample tasks may look like this: Determine the area of a circle with a diameter of 6 inches. O A. 9.42 square inches O B. 18.84 square inches O C. 28.26 square inches O D. 37.68 square inches

Circumference

Time Frame: March

Trimester 2 and 3


http://www.mathsisfun.com/definitions/circle.html

http://www.mathsisfun.com/definitions/pi.html


http://www.mathsisfun.com/definitions/circumference.html




Academic Vocabulary

Resources

6.4. Core Content: Two-and three-dimensional figures (Geometry/Measurement, Algebra) Link to OSPI Explanatory Comments and Examples 6.4.B Determine the perimeter and area of a composite figure that can be divided into triangles, rectangles, and parts of circles.

Sample tasks may look like this:



AND Math on Call





Academic Vocabulary

Resources

6.4. Core Content: Two- and three-dimensional figures (Geometry/Measurement, Algebra) Link to OSPI Explana tory Comments and Examples 6.4.C Solve single- and multi-step word problems involving the relationships among radius, diameter, circumference, and area of circles, and verify the solutions.

Sample tasks may look like this: Patricia is making 5 stools with circular seats that are each 12 inches in diameter. She wants to paint the tops of all the stools bright red, but needs to know the area she will paint. What is the total area of the tops of all 5 stools?

Diameter Radius



AND Math on Call


http://www.mathsisfun.com/definitions/diameter.html

http://www.mathsisfun.com/definitions/radius.html



Connected Math Unit: Variables and Patterns Following is a general outline of the 6th unit for Grade 6. In this unit, the focus is on mathematical expressions and equations. Extensive time

and effort are devoted to analyzing data sets showing change and describing the change in words. Students begin to write symbolic equations as a shorter, quicker way to give a summary of the relationship between two variable. The purpose of knowing the order of operation rules is

introduced. Standards Assessment/



6.2. Core Content: Mathematical expressions and equations (Operations, Algebra) Link to OSPI Explanatory Comments and Examples 6.2.A Write a mathematical expression or equation with variables to represent information in a table or given situation.


Dependent variable Equation Expression Independent variable Integer Order of Operations Pattern Relationship Rule

Connected Mathematics Unit Variables and Patterns AND

Math on Call Handbook AND Scott Foresman-Addison Wesley textbook 6.2.B

Draw a first-quadrant graph in the coordinate plane to represent information in a table or given situation.

Sample tasks may look like this: Tamyra is babysitting . She earns $3.00 for each hour. Draw a graph that represents her earnings at any point up to 30 hours. Be sure your graph includes: • A label for the vertical axis. • An appropriate and scale for the vertical axis • Draw points to represent the data and draw a line that

connects the point

Coordinates X axis Y axis

Time Frame: April Trimester 3

Tamyra’s Earnings

0 5 10 15 20 25 30 Hours Worked

http://www.k12.wa.us/Mathematics/Standards/WAMathStandardsGradesK-8.pdf#Page = 85

http://labwrite.ncsu.edu/po/dependentvar.htm

http://www.mathsisfun.com/definitions/equation.html

http://www.mathsisfun.com/definitions/expression.html

http://www.mathsisfun.com/definitions/independent-event.html

http://www.mathsisfun.com/definitions/integer.html

http://www.mathsisfun.com/definitions/order-of-operations.html

http://www.mathsisfun.com/definitions/pattern.html

http://www.icoachmath.com/math_dictionary/rule.html

http://www.mathsisfun.com/definitions/coordinates.html

http://www.mathsisfun.com/definitions/x-axis.html

http://www.mathsisfun.com/definitions/y-axis.html






6.2. Core Content: Mathematical expressions and equations (Operations, Algebra) Link to OSPI Explanatory Comments and Examples 6.2.C Evaluate mathematical expressions when the value for each variable is given.

Sample tasks may look like this: Evaluate x − 14 when x = 60. Write your answer on the line.

Variable


Math on Call Handbook AND Scott Foresman-Addison Wesley textbook

6.2.D Apply the commutative, associative, and distributive properties, and use the order of operations to evaluate mathematical expressions.


Distributive property Associative property Commutative property

What is x − 14 when x = 60? ____


http://www.mathsisfun.com/definitions/variable.html

http://www.mathsisfun.com/definitions/distributive-law.html

http://www.mathsisfun.com/definitions/associative-law.html

http://www.mathsisfun.com/definitions/commutative-law.html




Academic Vocabulary

Resources

6.2. Core Content: Mathematical expressions and equations (Operations, Algebra) Link to OSPI Explanatory Comments and Examples 6.2.E Solve one-step equations and verify solutions.

Sample tasks may look like this: Look at the equation below. 1.4y = 42

What is the value of y? O A. 30

O B. 40 O C. 41.6 O D. 43.4



6.2.F Solve word problems using mathematical expressions and equations and verify solutions.

Sample tasks may look like this: Lucinda earns $20 each week. She spends $5 each week and saves the rest. The table below shows the total amount that she saved at the end of each week for 4 weeks. Lucinda’s Savings at the End of Each Week

Week 1 2 3 4

Total amount Saved $15 $30 $45 $60

Lucinda continues to save at the same rate. Which expression represents Lucinda’s total amount saved at the end of n weeks?

O A. n + 15 O B. n x 15 O C. 20n − 5 O D. 25n





Academic Vocabulary

Resources

6.5. Additional Key Content (Numbers, Operations) Link to OSPI Explanatory Comments and Examples 6.5.B Locate positive and negative integers on the number line and use integers to represent quantities in various contexts.

Sample tasks may look like this: Look at the number line. P Q R S 0 2 Which letter on the number line corresponds to −4?

O A. P O B. Q O C. R O D. S

Integer Connected Mathematics Unit Variables and Patterns AND


6.5.C Compare and order positive and negative integers using the number line, lists, and the symbols <, >, or =.

Sample tasks may look like this: Which of the following numbers would make the statement correct? - 48 > ____

O A. - 50 O B. - 47 O C. -1 O D. 1


http://www.mathsisfun.com/definitions/integer.html



Connected Math Unit: How Likely Is It? Following is a general outline of the 7th unit for Grade 6. In this unit, the focus is on ratios, rates and percents. Students extend their knowledge of fractions to develop an understanding of what a ratio is and how it related to a rate and a percent. The unit has students continuing to work

with finding experimental probabilities and formally introduces theoretical probability.


Academic Vocabulary

Resources

6.3. Core Content: Ratios, rates, and percents (Numbers, Operations, Geometry/Measurement, Algebra, Data/Statistics/Probability) Link to OSPI Explantory Comments and Examples 6.3.A Identify and write ratios as comparisons of part-to-part and part-to-whole relationships.

Sample tasks may look like this: If a 250-piece puzzle has 70 border pieces, what is the ratio of border pieces to the total number of pieces in the puzzle?

O A. O B. O C. O D.

Ratio Connected Mathematics Units How Likely Is It? Investigations 1-3


6.3.B Write ratios to represent a variety of rates.

Sample tasks may look like this: Miss Hagman is having a BBQ. She has filled the ice chest with bottles of water and soda. There are 42 bottles in the ice chest and 12 of those are soda. What is the ratio of water bottles to soda bottles?

O A. 5:1 O B. 5:2 O C. 30:42 O D. 42:12

Time Frame: May - June Trimester 3


http://www.mathsisfun.com/definitions/ratio.html




Academic Vocabulary

Resources

6.3. Core Content: Ratios, rates, and percents (Numbers, Operations, Geometry/Measurement, Algebra, Data/Statistics/Probability) Link to OSPI Explantory Comments and Examples 6.3.F Determine the experimental probability of a simple event using data collected in an experiment.

Sample tasks may look like this: The water company is testing the wells in the area. They tested 7 wells and 2 of those needed purification. It is estimated that 140 homes in the area have their own wells. About how many do you predict will need purification?

O A. 10 O B. 20 O C. 40 O D. 70

Experimental probability: refers here to the relative frequency that was observed in an experiment.

Connected Mathematics Units How Likely Is It? Investigations 1-3


6.3.G Determine the theoretical probability of an event and its complement and represent the probability as a fraction or decimal from 0 to 1 or as a percent from 0 to 100.

Sample tasks may look like this: There is a bag with 9 tiles. The tiles have the following letters, one letter on each tile: A, B, C, E, G, H, I, L, and O. If one tile is selected at random, what is the probability that it will be a consonant?

O A. 0 O B. O C. O D.


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