SFUSD Mathematics Core Curriculum Development Project · 2020-02-17 · 2 SFUSD Mathematics Core...

1

SFUSD Mathematics Core Curriculum, Grade 5, Unit 5.3: Addition and Subtraction, 2014–2015

SFUSD Mathematics Core Curriculum Development Project

2014–2015

Creating meaningful transformation in mathematics education

Developing learners who are independent, assertive constructors of their own understanding

2


Grade 5

Unit 5.3: Addition and Subtraction

Number of Days

Lesson Reproducibles Number of Copies

Materials

1 Entry Task 1 Adding Using Multiple Methods 1 per student 2 Lesson Series 1 EM Journal p 32-33 (2 pages)

Adding and Subtracting Worksheet EM Journal p 35 EM Student Resource Book p 331

EM Journal 1 per student EM Journal EM SRB

Number cards 0-9 (4 of each) Calculators

2 Apprentice Task 1 Entry Task 2

Book Order (3 pages) Clock Fractions

1 per student 1 per student

1 copy of a Book order form per student

5 Lesson Series 2 EM Journal p 134-135 (2 pages) EM Student Resource Book p 198 EM Fraction Capture Masters p 460-461 (2 pages) Pattern Block Fractions (3 pages) EM Journal p 251-252 (2 pages) Exit Slips Worksheet of Addition of Mixed Numbers

EM Journal EM SRB 1 per student 1 per pair EM Journal 1 per pair 1 per pair

Construction Paper – 5 different colors, 1 sheet per pair, cut up ahead of time 1 cube per pair Pattern Blocks

1 Apprentice Task 2 Exploring Fraction Relationships 1 per student

2 Lesson Series 3 EM Journal p 254-255 (2 pages) EM Master p 488 Exit Slips Fraction Sentence pg. 16 Worksheet of Subtraction of Mixed Numbers

EM Journal 1 per pair 1 per pair 1 per pair 1 per student

Dice – either print from resources on cardstock, or used blank dice (8 per group) with sticky dots to label

1 Expert Task Digits to Fractions 1 per student

1 Lesson Series 4 EM Master p 470-471 (2 pages) EM Journal p 262 EM Student Resource Book p 322 EM Progress Check p 159

1 per pair EM Journal EM SRB 1 per student

1 Milestone Task EM Assessment p 193 Cindy’s Cats (2 pages)

1 per student 1 per student

3


Unit Overview

Big Idea

With the attention to place value, understand that adding and subtracting decimals has the same process as adding and subtracting any whole number. When two fractions have unlike denominators, equivalent forms will be needed for both fractions before fractions can be added or subtracted.

Unit Objectives

● Students will be able to write simple expressions involving whole numbers, decimals, and fractions. ● Students will be able to add and subtract number sentences by use of models, number lines, and manipulatives. ● Students will be able to add and subtract unlike fractions by using equivalent values.

Unit Description

This unit begins with a review of place-value concepts for whole numbers and decimals to the hundredths place and practice of these concepts in the use of the partial-sum method, partial difference, and trade first method. This is followed with the learning of the concept of adding and subtracting fractions of unlike denominators.

CCSS-M Content Standards

Operations and Algebraic Thinking Write and interpret numerical expressions. 5.OA.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 x (8 + 7). Recognize that 3 x (18932 +921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. Number and Operations in Base Ten Perform operations with multi-digit whole numbers and with decimals to hundredths. 5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Number and Operations—Fractions Use equivalent fractions as a strategy to add and subtract fractions. 5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) 5.NF.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < ½.

4


Progression of Mathematical Ideas

Prior Supporting Mathematics Current Essential Mathematics Future Mathematics

Students have had experience with the connection between decimal notation and fractions. They have also had experience with fluently adding and subtracting whole numbers. Additionally, they have practiced finding equivalent fractions and adding with like denominators.

Students will be identifying the differences and relationship between whole numbers, decimals, and fractions. Having the prior knowledge of finding equivalent fractions, students will learn the concept of adding and subtracting unlike fractions.

Students will use the knowledge they have gained in fifth grade and write expressions using variables. They will also compute and interpret expressions using different operations for decimals and unlike fractions.

5


Unit Design All SFUSD Mathematics Core Curriculum Units are developed with a combination of rich tasks and lessons series. The tasks are both formative and summative assessments of student learning. The tasks are designed to address four central questions: Entry Task: What do you already know? Apprentice Task: What sense are you making of what you are learning? Expert Task: How can you apply what you have learned so far to a new situation? Milestone Task: Did you learn what was expected of you from this unit?

1 day 2 days 2 days 5 days 1 day 2 days 1 day 1 day 1 day Total: 16 days

Entr

y Ta

sk 1

Lesson Series 1 A

ppre

ntic

e Ta

sk 1

En

try

Task

2

Lesson Series 2

A

ppre

ntic

e Ta

sk 2

Lesson Series 3

Ex

pert

Ta

sk

Lesson Series 4

M

ilest

one

Task

6


Entry Task 1. Adding & Subtracting Whole Numbers &

Decimals Using Multiple Methods, 2. Fractions on Clocks

Apprentice Task 1. Book Club Shopping Order,

2. Exploring Fraction Relationships

Expert Task Digits to Fractions

Milestone Task Egyptian Math & Cindy’s Cats

CCSS-M Standards

5.OA.2, 5.NBT.1, 5.NBT.7 5.NBT.7, 5.NF.1, 5.NF.2 5.NF.1, 5.NF.2 5.OA2, 5.NBT.7, 5.NF.1, 5.NF.2

Brief Description of Task

1. Students will be able to compute the addition of two decimals, compare the value of numbers using methods such as number lines, partial-sum method, and estimation, to name a few. 2. Students will be able to read a clock and identify the equivalence of each unlike fraction.

1. Students will be able to compute the addition and subtraction of multiple decimals in real-life situations. 2. Students will be able to find an equivalent fraction by means of adding unlike fractions.

Students will be able to add and subtract fractions to demonstrate their understanding of fractions by creating fractions with given digits, which makes each number sentence true.

Students will be able to display their knowledge of writing expressions by adding and subtracting with decimals and fractions with unlike denominators.

Source 1. Teacher Created Materials 2. TERC Investigations: Name that Portion

1. Teacher Created Materials 2. Adapted from Future Basics: Developing

Numerical Power by Randall Charles and Joanne Lobato; NCSM Publication

Nimble with Numbers Everyday Mathematics Open Response Unit 8 MARS Tasks 2007

Lesson Series 1 Lesson Series 2 Lesson Series 3 Lesson Series 4

CCSS-M Standards

5.NBT.7 5.NF.1 and 5.NF.2 5.NF.1 and 5.NF.2 5.NF.1 and 5.NF.2

Brief Description of Lessons

Review the relationship between whole numbers and decimals; identify the value of whole numbers in relation to decimals and vice versa.

Students will be able to explore and apply the concept of equivalent fractions to use the mathematical operation of addition.

Students will be able to explore and apply the concept of equivalent fractions in order to use the mathematical operations of subtraction.

Review of decimals, addition, and subtraction of fractions.

Sources

http://www.wccusd.net/

• http://bama.ua.edu/ • http://www.wccusd.net/ • http://www.youtube.com • http://www.teachingwithamountainview.com • http://www.math-aids.com/ • Teacher created exit slips

http://www.math-aids.com/ Teacher created exit slips for Subtraction of Mixed numbers with regrouping

7


Entry Task #1

Adding with Multiple Methods

What will students do?

Mathematics Objectives and Standards Framing Student Experience

Math Objectives: ● Students will be able to demonstrate their knowledge of adding decimals using

at least two methods (number line, partial-sum method, pictures, regrouping, base-ten blocks). CCSS-M Standards Addressed: 5.OA.2, 5.NBT.1, 5.NBT.7 Potential Misconceptions:

● 285 is equal to 2.85. ● Place value doesn’t matter when adding or subtracting decimals. ● The longer a decimal is, the greater it is in value. ● 2.85 consist of two whole numbers, 2 and 85. ● Whole numbers never include a decimal.

Launch: ● Students will be represented with two equations: 345 + 567 and 34.5 + 5.67. ● 30-second observations Think Pair Share, then whole class. If not mentioned,

get class to observe that the equations involve the same digits, but one equation involves whole numbers and the other involves decimals.

● 5-minute list on board: Knowing that these two equations are different, pose this question to students, “What is different about adding whole numbers and adding decimal numbers?” (Answers may vary; look for misconceptions).

● Students work with elbow partner listing what they know. ● List responses on board and debrief. ● Instruct students that they will individually demonstrate their knowledge of

adding decimals in at least two ways in the given task. During:

● Students will attempt the computation of the two equations and demonstrate in at least two ways how they are different. Their choices include number lines, expanded notation, estimation, and a method chosen by the student that has not been represented. Closure/Extension:

● Students choose one of their favorite methods demonstrated on their worksheet and copy it on a poster. Title includes the name of their method and all math work.

● All students participate in a gallery walk using small Post-it notes to comment and question using given sentence frames.

● Lead students to make some real-world connections, e.g., money. ● Include a Math Parking Lot (I’m curious about I wonder I’m unclear about...) for

further questions.

8


Adding & Subtracting Whole Numbers & Decimals Using Multiple Methods

How will students do this?

Focus Standards for Mathematical Practice: 2. Reason abstractly and quantitatively. 8. Look for and express regularity in repeated reasoning

Structures for Student Learning: Academic Language Support:

Vocabulary: method, number line, part-part whole, partial sum method, estimation, decimal, whole number Sentence frames: My idea is similar to _____ because... I disagree with ____ because... I’m unclear why/about... What I hear _________ saying is...

Differentiation Strategies: Participation Structures (group, partners, individual, other): Individual, partners, group

9


Lesson Series #1

Lesson Series Overview: Review the relationship between whole numbers and decimals; identify the value of whole numbers in relation to decimals and vice versa. CCSS-M Standards Addressed: Perform operations with multi-digit whole numbers and with decimals to hundredths. 5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Time: 2 days

Lesson Overview – Day 1 Resources

Description of Lesson: Students will be able to review place value concepts and write numbers in expanded notation. They review addition of whole numbers and decimals with partial sums and the column-addition method. Notes: Focus on place value and expanded notation (adding with partial sums strategy).

Everyday Mathematics 2.2, Addition of Whole Numbers and Decimals In class: Everyday Mathematics Math Journal, pp. 32–33 Homework: Adding/Subracting Worksheet From West Contra Costa County http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/general%20mathematics%20resources/AddingSubtractingModelsWorksheet.pdf


Description of Lesson: Students will be able to review the trade-first method and partial-difference methods in subtracting decimals. Notes: Use the Student Reference Book from Everyday Math to go over the trade-first and partial difference method.

Everyday Mathematics 2.3 Partial Differences In class: Everyday Mathematics Math Journal, p. 35 and Subtraction Target Practice Game. Homework: Teacher created number sentences to demonstrate different subtraction methods.

10


Apprentice Task #1

Book Club Shopping Order



Math Objectives: Students will be able to compute the addition and subtraction of multiple decimals in real-life situations.

● Students will be able to estimate the sum and difference of decimals. ● Students will be able to add and subtract decimals up to the hundredths.

CCSS-M Standards Addressed: 5.NBT.7, 5.NF.1, 5.NF.2 Potential Misconceptions:

● Place value is not important. ● Estimation of each purchase does not mean rounding to the nearest whole

number. Teacher Notes: Modification may be needed if the order forms you will be using are in whole numbers. Adjust the monetary value of the cost by increasing or decreasing by 1 or 2 cents. So, instead of $1, it will be $0.99 or $0.98.

Launch: Provide each student with a copy of an Scholastic Book order form. Students will be told they have $100.00 to spend on buying books through Scholastic Books using an Scholastic Book order form. They must purchase at least five different titles, keep a running record of their purchases (subtraction from $100), and must spend no less than $75.00 (ensures that students refrain from choosing only $1 titles). In addition, instruct students to purchase two copies of two of their selected titles (an additional opportunity to practice addition of decimals and extension component). During: Students use estimation to check that they are working within their $100 budget then subtracting each title’s price from the balance (a running total). Finally, students apply their knowledge of adding decimals by filling out their book order form which will also allow students to check if they have kept within their given budget as well as their subtraction in their running total. Closure/Extension: Students will cut out the pictures of their purchases and along with their order form (which shows their math), create a poster to share with their classmates on a gallery walk. Gallery visitors make inquiries and make constructive comments and suggestions on Post-it notes using appropriate sentence frames. Extension: Students may demonstrate on their poster a secondary method of adding and/or subtracting decimals other than what is demonstrated on their order form. Extension: Students may demonstrate multiplication of decimals on an extension order form.

11


Book Club Shopping Order


Focus Standards for Mathematical Practice: 2. Reason abstractly and quantitatively. 6. Attend to precision.


Vocabulary: decimal, place value, balance, sum, difference, running total, budget Sentence frames I appreciate … I like that you... I wonder why … I am curious about … What would happen if …? What is your thinking behind …? I disagree with your calculation of ….

Differentiation Strategies: Start students off with 1 example of the book ordering selections. Participation Structures (group, partners, individual, other): Individual, partner work

12


Entry Task #2

Fractions on Clocks



Math Objectives: ● Students will be able to find equivalent fractions that represent the rotation of

one hand around a clock face. ● Students will be able to find the sum of two fractions using a clock face when

playing a game of adding 2 fractions. CCSS-M Standards Addressed: 5.OA.2, 5.NF.1 Potential Misconceptions:

● Equivalent fractions do not share a common factor or multiple. ● Equivalent fractions are equal to each other when the denominator is the

same. ● Adding fractions involves adding the numerators together and adding the

denominators together regardless of the size of the whole.

Launch - Part 1: ● Introduce the task by having students refer to a clock face to explore twelfths by

looking at rotations of the hour hand while the minute hand is fixed at 12. ● Review that twelfths mean the 12 will be the denominator and why it is the

denominator. ● Keep an equivalent fraction poster, adding student contributions of twelfths and

equivalents of twelfths if given. ● Continue to manipulate the clock face (e.g., from twelfths to fractions of an hour

with minute hand not fixed at 12), adding to the equivalence poster and eliciting equivalents of fractions if not given by students. During - Part 1:

● Students will work individually on Clock Fractions student worksheet, writing fractions that tell how far the hand on each clock has moved.

● Students write as many equivalent fractions for each clock as they can. ● Circulate and observe student thought processes. ● Add to equivalence poster any fractions omitted by students and challenge

them to figure out which clock the fractions belong to. Closure/Extension - Part 1:

● Project the student worksheet template on an overhead or ELMO and asks students to give answers to each clock.

● Think about what they notice about each set of equivalent fractions under the clock faces. Is there a relationship with any of the numbers in the fractions? If so, what are they? If not, why not? Students pair up and share their thinking using a given sentence frame, then share their partner’s thinking using the given sentence frame.

● Point out that fractions that name the same amount are equivalent, or equal to each other. Represent this equivalence by writing equal signs between each equivalent fraction.

● Ask students to add equivalent fractions to the poster with their reasoning shared with the class.

13


Launch - Part 2:

● Draw students’ attention to the class clock face again. Tell students they are going to use the same clock face to add fractions.

● Ask, “If the hand moved one third of the way around the clock, and then moved one sixth more, where will it end up? What fraction has it moved altogether, and how can we represent this in an equation?

● Write the equation on the board: ⅓ + ⅙ = During - Part 2:

● Students think about the problem and then share their ideas with a partner using sentence frames. Students refer to their student worksheets from Part 1 if needed. Partners share out with class using sentence frames.

● If students focus on hours, ask them to consider minutes, leading an exploration of additional fraction addition problems on the board. Students may work in pairs and may use the clock faces to help solve the problems. Closure/Extension - Part 2:

● Goal: Students arrive at the understanding that moving ¼ of the way around is 3 o’clock and then moving ⅓ is 4 more, or 7 o’clock. This is equivalent to moving 7/12 of the way around the clock.

● Present mixed number addition problems.

14


Fractions on Clocks


Focus Standards for Mathematical Practice: 2. Reason abstractly and quantitatively 7. Look for and make use of structure


Vocabulary: equivalent fraction, denominator, numerator, factor, multiple, divide, multiply, equivalence, minute hand, hour hand, rotation Sentence frames: I know that ________________ is equivalent to ___ because... I noticed/did not notice that the equivalent fractions have a relationship to each other because. My reason is... __________ observed that … Please show us how you ________________________. Please clarify, _______, how you found your answer.

Differentiation Strategies:

● Student completes a certain portion of the worksheet depending on needs. ● Provide students with a list of equivalent fractions for two face clocks, and have student determine which clock each fraction represents.

Participation Structures (group, partners, individual, other):

● Individual, pairs, whole class

15


Lesson Series #2

Lesson Series Overview: Students will be able to explore and apply the concept of equivalent fractions to use the mathematical operation of addition. CCSS-M Standards Addressed: Number and Operations—Fractions Use equivalent fractions as a strategy to add and subtract fractions. 5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) 5.NF.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < ½. Time: 5 days Advance Preparation: Prepare 5 different colored construction papers cut in length of 2” by 18” for each student.


Description of Lesson: ● Review the relationship of fractions: part to whole. Numerator is the part; denominator is the

whole; which names the number of equal parts into which your whole is divided (dependent on what your whole is).

● Students will create their own fraction strips (aka fraction tiles, fraction bars) to explore the concept of equivalent fractions. Notes:

● **Materials MUST be prepped IN ADVANCE of this lesson. Organize students in pairs or small groups. Each student needs 5 3x18 inch strips of construction paper in five different colors, a pair of scissors and a number 10 envelope. (4 strips can be cut from a 12x18 inch sheet of construction paper.) Also prepare fraction dice—cubes with six faces labeled as follows: ½, ¼, 1/8, 1/8, 1/16, 1/16; each pair or group needs one cube.

● Refer to the “The Fraction Kits” on pp. 271–273 of About Teaching Mathematics by Marilyn Burns for a detailed teacher explanation of materials needed and the “Cover Up and the Uncover” activities.

● To follow up on this activity, you can continue to explore using the West Contra Costa County

How to Create Fraction Kits by Marilyn Burns http://bama.ua.edu/~crkraft/Math208/creating_fraction_kits.pdf About Teaching Mathematics by Marilyn Burns, pp. 271–273, The Fraction Kits activity. West Contra Costa County (focus only on method #1): http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/lessons/grade%205%20lessons/AddingFractionUnlikeMultipleAlgorithmsV2.pdf

16


activity focusing on method #1 with fraction tiles only. Method #2 is focused on common denominators and can also be presented at a later point, but not in day 1. Method #3 uses vocabulary and a strategy that can be confusing, so please use this as an extension only if appropriate for your class.

● Have students use the fraction strips to get sums of 1 and sums with less than 1.


Description of Lesson: ● Students will be able to apply multiplication and division rules to find equivalent fractions. This is

conceptually based on being able to multiply or divide by a whole, which will always yield an equivalent fraction.

● Students can begin the lesson with an activity of creating a number line, where they will be guided to write the equivalent fractions on it. For example: ½ = 2/4 = 3/6 = 8/16. Notes:

● Materials MUST be prepped IN ADVANCE: Use a 8 ½” x 14” paper that can be used for the number line activity.

● The number line activity works best with an 8-1/2 x 14” sized paper that students can fold. They begin with the ½ mark on the number line; continue with the 1/4s, then the 1/8s, and 1/16s. Along the way, pointing out the equivalency that exist and marking them on the number line. For example: ¼ = 2/8 = 4/16. Students will work in pairs and play a game that will enable students to add and subtract fractions as well as compare fractions.

Everyday Mathematics 5.4, The two rules for finding equivalent fractions.

In class:

1. Number Line activity (need 8 1/2 “ x 14” sized paper) 2. Everyday Mathematics Math Journal pp. 134–135

Extension: Fraction Capture Game: Student directions in their Math Journal p. 198 and the game board and record sheet are in the Everyday Mathematics Math Masters pp. 460–461.) YouTube Video to explain the Fraction Capture game: http://www.youtube.com/watch?v=L0sovX62e_0


Description of Lesson: Students will work in pairs to complete an activity worksheet using pattern blocks to find equivalent fractions to add fractions with different denominators. Notes:

● The first two problems will be done whole class with the activity worksheet projected on the board, which allows for modeling, conceptual understanding, and any student questions or comments.

● This lesson will not address mixed numbers and improper fractions. The pattern block activity will be used on Day 9 to introduce this concept.

● Students will need pattern blocks and colored pencils

Pattern Block Fraction Activity: http://www.teachingwithamountainview.com/2013/03/our-latest-fraction-projects.html

17



Description of Lesson: Addition with Renaming the Fraction Students will develop addition concepts related to mixed numbers. Students will review fraction addition by adding mixed numbers in which the fractional parts have like or unlike denominators and rename the sums in simplest form. Notes: Begin with a number talk to get the students in the motion of talking about how to find common denominators. Some examples and number models are made ready to use or create your own to use with your students.

● This lesson is a continuation of Day 3. ● Refer to the pattern block activity to address mixed numbers specifically on #3 and #4 on the

worksheet from the website Pattern Block Fraction Activity.

West Contra Costa County: http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/general%20mathematics%20resources/AddingSubtractingModelsWorksheet.pdf Pattern Block Fraction Activity: http://www.teachingwithamountainview.com/2013/03/our-latest-fraction-projects.html Homework: Everyday Mathematics 8.2, Adding Mixed Numbers In class: Everyday Mathematics Math Journal, pp. 251–252 Use Exit Slip template with one problem to give students an opportunity to demonstrate understanding of the concept.


Description of Lesson: Students will be able to add mixed numbers and convert their sum in the form of improper fractions to mixed numbers. Notes: Begin with a number talk to get the students in the motion of talking about how to find common denominators and add the fractions. Some examples and number models are made ready to use or create your own to use with your students.

● Students will need to convert improper fractions to mixed numbers in the solution. ● ● Use the online worksheet creation website if you want to create homework or additional practice

worksheets.

Online Worksheet printable (problems with an answer key): http://tinyurl.com/AddingMixedNumbers Online Worksheet creation website – to generate your own worksheet: http://www.math-aids.com/Fractions/Adding_Mixed_Numbers.html Homework:

18


Apprentice Task #2

Exploring Fraction Relationships



Math Objectives: ● Students will be able to demonstrate their knowledge of fractions by using

different measures of fractions to find a fraction (by drawing, illustrating and writing). CCSS-M Standards Addressed: 5.NF.1, 5.NF.2, 5.OA.2 Potential Misconceptions:

● All fractions can be added straight through, including denominators.

Launch: ● Introduce the task by having students read the given tasks. ● Students do a quick write about what they know about each fraction. ● Students will be given 10 minutes to construct ¾ as many different ways as

possible. During:

● Students will share out their ways of getting to ¾ with the given measurements and discuss the reason why it works. Closure/Extension:

● Students identify the different relationship between fractions with unlike denominators to the unit fraction.

● Students create a poster to share their knowledge of fractions. Then do a gallery walk to appreciate others’ work. Extension: The fraction of the sugar may change, or one of the measuring cups can be missing.

19


Exploring Fraction Relationships


Focus Standards for Mathematical Practice: 2. Reason abstractly and quantitatively. 6. Attend to precision.


Vocabulary: equivalent fraction, denominator Sentence frames: I have __________________. I know that ________________ because ____________. One way to show _______ is _____________________. Please show us how you ________________________. Please clarify, _______, how you found your answer. I appreciate …/ I like that you... I wonder why … I am curious about … What would happen if? What is your thinking behind? I disagree with your calculation of.

Differentiation Strategies:

Participation Structures (group, partners, individual, other):

● Students can work in pairs to discuss the relativity of each fraction, ordering from least to greatest. ● Students will work individually to find the different ways of making ¾ cup of sugar.

20


Lesson Series #3

Lesson Series Overview: Students will be able to explore and apply the concept of equivalent fractions in order to use the mathematical operations of subtraction. CCSS-M Standards Addressed: Number and Operations—Fractions Use equivalent fractions as a strategy to add and subtract fractions. 5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) 5.NF.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < ½. Time: 2 days


Description of Lesson: Students will subtract fractions with unlike denominators. Students will be reviewing mixed numbers to be decomposed to facilitate the ability to do the subtraction. Afterward, students will use their Math Journal page and the game to solidify their understanding. Notes: Begin with a number talk to get the students in the motion of talking about how to subtract with fractions. Some examples and number models are made ready to use or create your own to use with your students. Review mixed numbers in relation to renaming before subtracting. For example, 8 - 3 ⅔ ==> 7 3/3 - 3 ⅔

Everyday Mathematics 8.3, Subtracting Mixed Numbers In class: Everyday Mathematics Math Journal, p. 254 Game: Mixed Number Spin. Students use the Everyday Mathematics Math Journal, p. 255. You will need a copy of the Math Master p. 488 for the spinner. Homework: In class: Use Exit Slip template with one problem to give students an opportunity to demonstrate understanding of the concept.

21


Lesson Overview – Day 2 Suggested Resources

Description of Lesson: Subtraction of Unlike Fractions with Regrouping Students will apply their knowledge of unlike fractions to work on subtraction expressions. Then students can apply their understanding to practice adding, subtracting, and comparing fractions through Fraction Sentences activity. Notes:

● **Materials MUST be prepared IN ADVANCE of this lesson. ● All students need a copy of pg. 16 - Fraction Sentences (included in consumables) ● 3 copies per group of pg. 17 (Fraction Sentence Cube A) – on cardstock ● 2 copies per group of pg. 18 (Fraction Sentence Cube B) – on cardstock ● **NOTE: Instead of copying the above pages on cardstock, you can use 8 die per

group and label the sides with sticky dots. This will avoid yearly reproduction of pgs. 17-18.

● Begin with a number talk to get the students in the motion of talking about how to subtract with fractions. Some examples and number models are made ready to use or create your own to use with your students.

● The Fraction Sentences activity may be done with a partner or individually. Use cardstock paper or blank dice with circle stickers (if available) to create the fraction dice.

Teacher reference explanation: West Contra Costa 5th grade lessons website: http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/l

essons/grade%205%20lessons/SubtractingMixedNumbersV4.pdf Fraction Sentences Subtraction of Mixed Numbers worksheet for extra practice Homework:

22


Expert Task

Digits to Fractions



Math Objectives: Students will be able to add and subtract fractions to demonstrate their understanding of fractions by creating fractions with given digits, which makes each number sentence true. CCSS-M Standards Addressed: 5.NF.1, 5.NF.2 Potential Misconceptions:

● Students may choose the incorrect digit to make a fraction that will not get to the specified sum.

● Students may not use estimation as a strategy in selecting the correct digits for their fractions.

● Students may add denominators instead of finding the common denominator to find the sum.

Launch: ● Students will be given four digits (1, 2, 4, 5) to use only once in each equation

to create fractions that make each equation true. Working with partners, students will have the opportunity to create fractions with the given digits to try to find the specified sums and make the equation true.

● Students will use multiple representations to prove their work. Students will be able to use fraction strips, a number line, algorithms, etc., to justify their work. During:

● After all students have solved #1 and #2, regroup the class, and have students (either volunteers or ones that you select) share their mathematical thinking and multiple representations with the entire class.

● Students will continue to solve #3–6 on the Digits to Fractions worksheet. Closure/Extension:

● At the end of the activity, students will be able to share out their thinking and how they came up with the correct digit to make the fractions that were able to make the equation true.

● Students will be able to show their multiple representations for #3–6.

23


Digits to Fractions


Focus Standards for Mathematical Practice: 1. Make sense of problems and persevere in solving them. 7. Look for and make use of structure.


Vocabulary: digits, equation, sum, multiple representations Sentence frames: I used the representation of ________________ to show that _________ plus __________ equals ____________. Using (name of representation) _______________, I can justify that _________ plus ___________ makes my equation true. My equation for number ________ is true because _________________________. I chose to use (name of representation) _____________ to support my work for number ________ because __________________. To prove that _________ added to _________ equals ___________, I chose the representation of _________________ because ___________. I used the representation of ________________ in order to show that _________ minus __________ equals ____________. Using (name of representation) _______________, I can justify that _________ minus ___________ makes my equation true. To prove that _________ subtracted from _________ equals ___________, I chose the representation of _________________ because ___________.

Differentiation Strategies: Participation Structures (group, partners, individual, other):

24


Lesson Series #4

Lesson Series Overview: Review of decimals, addition, and subtraction of fractions. CCSS-M Standards Addressed: Number and Operations—Fractions Use equivalent fractions as a strategy to add and subtract fractions. 5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) 5.NF.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < ½. Time: 1 day


Description of Lesson: In today’s lesson, students will apply their knowledge of adding and subtracting mixed numbers to play the Fraction Spin game. Students will also need to review adding and subtracting decimals. Notes:

● For this review day, use a game for the fraction review, which will solidify student understanding of addition and subtraction of fractions.

● For decimals, students can use the Everyday Mathematics Unit 2 Progress Check as a review and be able to apply multiple strategies.

Everyday Mathematics Fraction Spin Game in Math Masters, pp. 470–471 (Student Math Journal, p. 262) Explanation of the game is in the Student Reference Book under the game section labeled Fraction Spin. Decimal Review: Everyday Mathematics Unit 2 Progress Check, p. 159, only uses the 6 problems that are on the Written Assessment portion of Unit 2 Progress Check.

25


Milestone Task

Writing Egyptian Fractions & Cindy’s Cats



Math Objectives: Students will be able to display their knowledge of writing expressions by adding and subtracting with decimals and fractions with unlike denominators. CCSS-M Standards Addressed: 5.OA.2, 5.NBT.7, 5.NF.1, 5.NF.2 Potential Misconceptions:

● Use only one unit of each fraction ½, ⅓, ¼, etc. Students may try to use ⅖ or ¼ more than once. Teacher Notes:

Even though these are 2 different tasks, you will be able to evaluate how students demonstrate their knowledge of showing multiple representations. *Rubrics for both Writing Egyptian Math and Cindy’s Cats are within the file.

Launch: ● Begin by doing a choral read of the Writing Egyptian Math. Allow students to

ask clarifying questions. Thoroughly explain that a unit fraction is just one unit. ● Suggest that they do not have to start with the next largest unit fraction. Once

they have followed the process through the first time, they will have to look for another combination the second time.

● Remind students to show all work when working on Cindy’s Cats. ● Students will use multiple representations to prove their work. Students will be

able to use fraction strips, a number line, algorithms, etc., to justify their work. During:

● Walk around the classroom to assure that students are on the right track. ● Remind students to try to find multiple ways to find fraction-addition number

sentences. Closure/Extension:

● Upon completion, students will share out their findings and methods of finding 9/10 using one unit of each fraction.

● Students will explain other ways and representations of their answers in written form.

26


Writing Egyptian Fractions & Cindy’s Cats



Vocabulary: Sentence frames: I used the representation of ________________ to show that _________ plus __________ equals ____________. Using (name of representation) _______________, I can justify that _________ plus ___________ makes my equation true. My equation for number ________ is true because _________________________. I chose to use (name of representation) _____________ to support my work for number ________ because __________________. To prove that _________ added to _________ equals __________, I chose the representation of _________________ because ___________. I used the representation of ________________ to show that _________ minus __________ equals ____________. Using (name of representation) _______________, I can justify that _________ minus ___________ makes my equation true. To prove that _________ subtracted from _________ equals ___________, I chose the representation of _________________ because ___________.

Differentiation Strategies: For Egyptian Math, have students describe how they might find multiple ways of writing 9/10 as a sum of the unit fractions. For example, each time I will start with a unit fraction that I have not used. Then I know the combination will be different. Participation Structures (group, partners, individual, other): Individual Work Resources: Everyday Mathematics Unit 8 Open Response, Assessment Handbook, p. 193 Optional constructed response questions in the resource folder online: Constructed Response examples (West Contra Costa): http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/common%20core%20mathematics%20resources/Grade%205%20Selected%20Response%20Items/Gr5sr5NF1.pdf Selected Responses examples (West Contra Costa): http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/common%20core%20mathematics%20resources/Grade%205%20Selected%20Response%20Items/Gr5sr5NBT7.pdf

SFUSD Mathematics Core Curriculum Development Project · 2020-02-17 · 2 SFUSD Mathematics Core...

Documents

Transcript of SFUSD Mathematics Core Curriculum Development Project · 2020-02-17 · 2 SFUSD Mathematics Core...