By the end of this section, students should be able to perform operations with fractions and explain their strategies using previously mastered mathematical concepts.

Suggested pacing 5-6 weeks 

Teacher tips: 

• Area was covered in Q4, so you may want to go back and use similar problems but adding in fractional units (halves and fourths).

• Utilize visual models and the idea of groups of less than one BEFORE introducing any algorithms.

• Order of operations was covered in question 2 with whole numbers and question 3 with decimals, so you can revisit those resources and add in fractions.

sample pretest

Essential Learning Outcomes (ELO)

∎ Multiply and divide proper and improper fractions, and create equations from word problems. (5.NF.3, 5.NF.4.a, 5.NF.5 5.NF.6, 5.NF.7) (SMP1, SMP5)

∎ Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. (5.NF.4.b) (SMP1, SMP5) 

🌕 Use parentheses, brackets, or braces in numerical expressions with fractions, and evaluate expressions with these symbols. (5.OA.1) (SMP2, SMP5)

🌕 Write simple expressions that record calculations with fractions, and interpret numerical expressions without evaluating them. 

For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. (5.OA.2) (SMP2, SMP5)

Learning targets

• I can interpret and recognize fractions as division problems (5.NF.3)

• I can solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers by using visual fraction models and/or equations to represent the problem. (5.NF.3)

• I can use factors to estimate a product. (5.NF.3)

• I can use real world examples to explain multiplication of fractions by fractions and/or whole numbers. (5.NF.4.a)

• I can find the area of a rectangle by tiling unit squares (5.NF.4.b)

• I can compare  the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. 5.NF.5.a 

• I can explain  why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case) 5.NF.5.b 

• I can explain why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1. 5.NF.5.b 

• I can use real world examples to explain multiplication of fractions by fractions and mixed numbers by using visual fraction models or equations to represent the problem. (5.NF.6)

• I can divide fractions by whole numbers  and divide whole numbers by fractions using a visual fraction model. (5.NF.7)

• I can convert answers from improper fractions to mixed numbers. (5.NF.7) 

• I can use parentheses ( ), brackets [ ], and braces { } in numerical expressions with fractions. (5.OA.1)

• I can evaluate expressions with parentheses  ( ), brackets [ ], and braces { }  with fractions. (5.OA.1)

• I can write simple expressions that record calculations with fractions (5.OA.2)

• I can interpret numerical expressions  with fractions without evaluating them (5.OA2)

∎ Major Content           ⊡ Supporting Content           🌕 Additional Content

Computational Number Talks/Strings (minimum 3 days a week) to work on computational strategies.

5th grade number talk guide printable  &   3-5th grade number talks 

Add/Subt  &  Mult/Div Strategies   

Choose which strategy students need to practice.  You may find that they need many, so start with one for a week or so, then move onto another.  You are looking for efficient strategies, not mastery of all strategies.  Students may find they prefer one strategy over another or change strategies for different problems.  The goal is that they are flexibly using efficient strategies and are able to reason about numbers to fluently compute.

Multiplication Strategies Decimals  (Main focus)

  use partial products Partial products  mixed decimals

  break apart factors  tenths  hundredths

doubling/halving   Double & half

Fraction Strategies  (Main focus)

Add unlike denominators    Use area model to find like denominator     Number line       Benchmark ½       Benchmark of 1whole

Subtract like denominators  Like denominator      Partial difference

Multiply   unit fraction of whole    Breaking apart strategy  Doubling/Halving strategy 

MUST DO/Core Resources:  

Ready Teacher Toolbox        Lesson 19: Understand Multiplication by a Fraction-Sessions 1-3

   Lesson 20: Multiply Fractions to Find Area -Sessions 1-4

Assessment Tasks 5.NF.4,   Frayer Model Assessment           Proficiency Rubrics  5.NF.4a     5.NF.4b                      IAR sample questions 

CAN DO/Additional Resources:

Math in Practice:   5.NF.4,5,6 - Module 9     Math in Practice lesson slides and Essential Question Guide         MIP Resource folder

Word problems are difficult for many students.  The goal is to support students engaging in the context of the problem and going beyond looking for keywords and numbers.  Here is a resource that will support applying close reading with math:    Numberless Word Problems             Multiplication and Division Problem Types   (comparison with unit fractions)

Open Middle tasks Printable activities & Centers                 Nearpod Math lessons

Prior knowledge/Just in Time support     &     Enrichment RTTB    Lesson 19 Flower Garden &  Lesson 20 Colorful Quilts  

Interactive manipulatives

MUST DO/Core Resources:  

Ready Teacher Toolbox        Lesson 22: Multiply Fractions in Word Problems-Sessions 1-4

Assessment Tasks 5.NF.6,     Frayer Model Assessment           Proficiency Rubrics  5.NF.6                        IAR sample questions 

CAN DO/Additional Resources:

Math in Practice:   5.NF.4,5,6 - Module 9      Math in Practice lesson slides and Essential Question Guide         MIP Resource folder

Word problems are difficult for many students.  The goal is to support students engaging in the context of the problem and going beyond looking for keywords and numbers.  Here is a resource that will support applying close reading with math:    Numberless Word Problems             Multiplication and Division Problem Types   (comparison with unit fractions)

Open Middle tasks Printable activities & Centers                 Nearpod Math lessons

Prior knowledge/Just in Time support     &     Enrichment RTTB   Lesson 22 Plant Growth  

Interactive manipulatives

MUST DO/Core Resources:  

Ready Teacher Toolbox        REVIEW    Lesson 30: Evaluating, Writing, and Interpreting Expressions -Sessions 1-4

Assessment Tasks 5.OA.1      5.OA.2   Frayer Model Assessment           Proficiency Rubrics  5.OA.1       5.OA.2              IAR sample questions 

CAN DO/Additional Resources:

Math in Practice:   5.OA.1 & OA.2- Module 2      Math in Practice lesson slides and Essential Question Guide         MIP Resource folder

Open Middle tasks Printable activities & Centers                 Nearpod Math lessons

Prior knowledge/Just in Time support     &     Enrichment RTTB Lesson 30 Mystery Expression

Interactive manipulatives

Prior knowledge

4 NF4     Multiplying and Comparing   Parts of a Whole   

4 NF 1      Equivalent Fractions   Fraction Blackout  (center/game)

3 NF 3   Number line Madness

3 NF 1   Capturing Hexagons    Fraction Roll 'Em   Three in a Row

3 NF 2   Fraction Matchup

4 OA 1  Factors and Multiples  (center/game)  Squares Numbers (center/game)  (Spanish)

4 OA 2   Best Math Friends Game (p.86)

4 OA 3    Operation Arithemetic (p.86)    Karl's Garden

3 OA 5  Decomposing Factors for Partial Products   Turn Around Arrays   (Array Cards) 

3 OA 1 Double up (p. 3)  Tic Tac Toe Array (p. 4)   Raging Rectangles (p.8)    Snakes Alive (p.7)

3 OA 2   Murphy to Manteo7) (p.14)

3 OA 6   Find the unknown numbers (p.24)   Multiplication & Division Match

Nearpod Math lessons

Enrichment

• Inside Mathematics Problem Solving- leveled problems

These are activities to give students mixed, spaced practice based on the big ideas for 5th grade math.

Geometry (4th)

• • students can use geometry vocabulary cards to build shapes using anglegs, geoboards, or other manipulatives

  • Geo Matchup

  • Angle Estimation Competition

  • MLC Math at Home problem solving & games

Volume (5th Q4)

• • Rolling For Prisms 

  • MLC Math at Home problem solving & games

Spiral Practice

These resource sheets are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.   Please select pages carefully based on your students' needs. 

You may have students work on these with a partner, independently with an answer key to self-check (tip: use sheet protectors), or as a journal response.   It is not necessary to have students complete a page every day- the intent is to have opportunities to spiral concepts for mixed practice, not do "busy" work.

Multiply/Divide Decimals