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Fractions
CA Common Core Standards

Operations and Algebraic Thinking

Represent and solve problems involving multiplication and division.
CCSS.MATH.CONTENT.3.OA.A.1
Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
CCSS.MATH.CONTENT.3.OA.A.2
Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.
CCSS.MATH.CONTENT.3.OA.A.3
Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1
CCSS.MATH.CONTENT.3.OA.A.4
Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = _ ÷ 3, 6 × 6 = ?
Understand properties of multiplication and the relationship between multiplication and division.
CCSS.MATH.CONTENT.3.OA.B.5
Apply properties of operations as strategies to multiply and divide.2 Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)
CCSS.MATH.CONTENT.3.OA.B.6
Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.
Multiply and divide within 100.
CCSS.MATH.CONTENT.3.OA.C.7
Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
Solve problems involving the four operations, and identify and explain patterns in arithmetic.
CCSS.MATH.CONTENT.3.OA.D.8
Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.3
CCSS.MATH.CONTENT.3.OA.D.9
Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

1 See Glossary, Table 2.
2 Students need not use formal terms for these properties.
3 This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in conventional order when there are no parentheses to specify a particular order (Order of Operations).




Marilyn Burns Fraction Kit Day 1
This section is for Fractions (May)
*Note as a team we decide to start earlier (February/March) 
Lesson Summary
Students will be starting a fraction kit from five different colored strips, cutting them into halves, fourths, eighths, and sixteenths and leaving one strip whole.  Student will use the fraction kit to play, "Cover Up, and Uncover"



Math Focus Points
The purpose of this lesson is to familiarize students with equivalent fractions.

Fractions 
Investigatios Unit 7 

Week 1:
Day 1:
Session 1.1: Sharing Brownies 
 
Day 2 and 3:
Session 1. 2: Making Fraction 
This is similar to the fraction kits except they are folding 8 1/2 x 11 inch paper horizontally and vertically.  You could choose to skip this lesson but its likely to give students a more flexible understanding of fractions by providing a different model.  They also practice putting fractions in order.  

Day 4: 
Session 1.3: More than one Piece 

Day 5:
Session 1.4: Sharing Many Things
This lesson exceeds the standards as you are finding fractions of a group of objects.  However, it provides a nice connection to multiplication and division and it is rigorous.  You will have to decide if you want to teach it.  

Week 2
Number Line Sequence
Day 1:Investigations Session 1.4 A Number Lines

Day 2: Investigations Session 1.4 B Number Lines
Fractions on the Number Line (Cuisenaire Rod Lesson) Students can also write their own equivalent fractions and observations. 

Day 3: Comparing Fractions (ME 7-6 Student book p. 383-comparing halves,  fourth, and eights.  pg. 384 includes thirds and sixths) Fractions on the Number line 

Day 4: Bridges Session 4 pg. 23 
Fractions as distances (great lesson for number lines) 

Day 5: Bridges Session 5 pg. 29
Fractions on the Number line 
 Math Expressions, Unit 7 lessons 3-7 have some great number line experiences incorporating fraction such as 4/1 and 5/5.  

*Additional Lesson Sequences, depending on what your students need:
Choice A-Adding Fractions Investigations Unit 7: Investigations 2 (This investigation uses pattern blocks and focuses on adding fractions which is good for students, but beyond 3rd grade standards) 
2.1 Making Fraction Cookie Shares
2.2 The Fraction Cookie Game 


Additional Supplements 
Supplements 


Week 3:
Choice A-Adding Fractions
Investigations Unit 7 Investigation 2 (this investigation uses pattern blocks and focuses on adding fractions which is good for students beyond 3rd grade standards). 
2.1 Making Fraction Cookie​
2.2 The Fraction Cookie Game 
2.3 Assessment: Many Ways to Make a Share

Choice B-Deepen 
Understanding of thirds, sixths, twelfths, Make the rest of the fraction kit
Day 1: Fraction Kit-make thirds, sixths, twelfths
Day 2: Play Cover Up, Uncover V1 and V2 with thirds, sixths, twelfths.  
Day 3: Wipe-Out with Pattern Blocks
Day 4: Practice pages from Math Expressions
Day 5: Do some partitioning pages from Eureka and possibly some from Math Expressions 

Choice C- Select Lessons from Bridges in Mathematics, Unit 4, Module 3
Session 3 (p. 15)  Pattern Block Fractions "If the rhombus is 1/2 what is the whole?" 4D Hexagon Spin & Fill (game) 
Session 4 (p. 23) Fractions as Distances (great lesson for number lines)
Session 5 (p. 29) Fractions on the Number Line  
Week 1: Feb. 27-March 4
Graphs, Mass, elapsed time, volume (word problems) Rounding 
Math Expressions Unit 3
Addresses all of these topics.  Be sure to use these activities as they are similar to SBAC.  Line plots with mixed numbers and scaled have to choose a value for the scale.  
Mass and Volume: Investigations Unit 9, Sessions 4.1-4.3A 

May 6-10
Review or continue with measurement. Testing??
Unit 7 Lesson 3
Fractions on the Number Line TE pg. 766 (long lesson)
Student workbook pg. 375-376
May 13-17 
Fractions 
Session 1:
ME Unit 7 Lesson 3: Fractions on the Number Line 
Activities 1 & 2: Unit Fractions to locate Fractions and Fractions Greater than 1 on the Number Line 
& TE pg. 722. Student workbook pg. 377-378 (30 mins) Hw. 261-262 ME challenge Game TE pg. 755 (or activity below) 

Lines: In-class, every group of 3 students makes a set of fraction cards using index cards and these fractions: 1/2, 2/2, 3/2, 4/2, 1/4, 2/4, 3/4, 4/4, 7/4, 1/8, 3/8, 4/8, 7/8, 8/8 1/16, 5/16, 7/16, 15/16 2/1. 
Use the pre-marked lunch lines or Weds.  Class lines on the playground as the Number Lines and students work in groups to place their fractions on the number lines.  Once they are sure they have them in the correct places, they write the fractions in chalk.  
Encourage students to communicate and justify their thinking. 
Optional: Use the red fraction die to play a hopping game.  Students try to be the first one to get to the end of their number line.  Each student rolls the die and hops the size jump on the die and hops the size jump on the die or jumps equivalent to the fraction in the die (example: roll 1/2 and jump 1/4 and 1/4).  Or any variation of hopping games.  Maybe students can create their own game.  
Session 2: ME Unit 7 Lesson 4: 
Comparing Unit Fractions 
students workbook pg. 379-380 (40 mins.)
ME Challenge Fraction Card Activity (comparing Fractions) Hw. pg.  263-264

Exploration 
1.  Play "Capture Fractions," "War," with unit fractions.  You may need to have students write unit fractions on index cards to create your game sets.  
a.  On Level Card set (have students make 2 of each): 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/12, 1/16, 1/1
b.  Challenge Level Card Set ( use the unit fractions card set and have students make 1 card for each of these additional fractions):
2/4, 3/2
2/4, 3/4
2/3, 3/3
2/6, 3/6, 4/6, 5/6, 6/6
2/8, 3/8, 4/8, 5/8, 6/8, 7/8, 8/8 
4/12, 6/12, 11/12, 12/12
2/16, 8/16, 15/16
4/1, 100/1
Have students use the sentence frame "_____ is greater than/less than _____ because ________. " 

Session 3: Spiral Review-small group instruction, Fraction Games
*Independent workshop where students play any games you have already taught.  Teacher does small group intervention during this time.  

Session 4: ME Unit 7 Lesson 5:
Comparing Fractions (circles)
TE pg. 784
​Student Workbook pg. 381A-382 (45 mins.) 
HW pg. 265-266 
Options for Exploration 
-Investigations Unit 7, Session 2.1 (Making Cookie Share) (pattern blocks)
-Marilyn Burns 
Introduction Fractions-Play Wipeout (pattern blocks)-In Teacher Shared Folder 3rd.  Grade-math T3 Fractions-Wipeout 

Session 5: 
ME Unit 7 Lesson 7:
Equivalent Fractions on the Number Line 
TE pg. 800 Student workbook pg. 385-386 (60 mins.)  
Hw. pgs. 269-270
*This will reinforce the number line work we already did with the Cuisenaire Rods.  
May 22-29
Session 1: Review comparing fractions and give the "Comparing Fractions" portion of the T3 assessment.  
For the comparing fractions assessment: This assessment is designed to be administered as a formative assessment during the unit when you feel certain your students are ready to compare fractions using models and reasoning about fractions.  

Provide pre-cut models for students to choose from and glue on.  They can draw any model that makes sense for them instead of using a pre-made model if they choose.  Use the attached master (on the T3 test)
of the fraction strips, number lines, and circles to copy and cut out the model choices for students. 
Session 2: ME Unit 7 Lesson 8 Using Fractions to Solve Real World Problems (60mins.)
TE pg. 806 
Student workbook pg: 387, 388 
HW pg: 271-272
Session 3: Review Quadrilaterals 
*On the T3 assessment, students need to identify quadrilaterals and understand that a square is a also a rectangle, rhombus, and a quadrilateral. 
Number Talk:
2x10
2x20
2x30
2x40
ME Unit 6, Lesson 2, TE pg: 668: Naming Quadrilaterals (30 mins. lesson)
Homework book pg: 237 (use a  a "practrice test"/whole class review)
Adminster Questions 9,10, & 11 as  you culminate this lesson. 
Session 4: Review Fractions before T3 assessment:
In a whole-class review format, provide problems similar to question 1-8 on the T3 assessment. 
Discuss, justify, work on how to write an argument.  
Session 5: T3 test, Questions 1-8
Once all students are finished, go over test together.  Each student needs a colored pencil or pen.  Each student keeps his/her own test. Goal is to allow revisions, but be able to see the changes so we can score the original work.  Students may not erase what they have already done, but may add to it in a different color.  The teacher should not give answers, but instead post a problem and facilitate a discussion, allowing all students to engage in the math, learn from each other, and revise their answer, promoting self-assessment, opportunities for revision, and ownership of the learning.  
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