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Woodridge District 68 Curriculum
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Unit 5
multiplying & dividing partial Numbers                                                                   duration: 6 weeks



​Essential Questions:
  1. How can the change from a purchased be divide up between friends?
  2. How can you calculate how much a dozen boxes of candy costs?
Big Ideas:

Unit 5 instructional time is focused on these power standards.
5.NBT.B.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.​

5.NF.B.6
 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. 

5.NF.B.7.C Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? 
SAMPLE assessment items 5.NF.B


Unit 5 instruction is supported by the following standards:
5.NF.B.3 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? 

5.NF.B.4.A Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) 

5.NF.A.4.B 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.B.5.B Explaining 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); explaining 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.C.7.A Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. 

5.NF.C.7.B Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.

What to Teach

Unit 5 Outline
Pre-assessment
​Introduce Real World Experience
Topic 1 - Multiply Decimals (5 days)
  • I can use properties of operations and my knowledge of repeated addition to multiply decimals.
  • I can use my understanding that a decimal is a partial number to estimate if a product will be greater than, less than, or equal to the original number.
  • I can multiply decimals using concrete models or drawings.
  • I can use strategies based on place value to multiply decimals.
  • I can explain my thinking in writing when multiplying decimals.

Lesson Idea

Teaching Decimal Multiplicaton Video
​(w/ base ten block models)

Student PRactice

Word Problem Generator

Topic 2 - Divide Decimals (5 days)
  • I can use properties of operations and my knowledge of repeated subtraction to divide decimals.
  • I can divide decimals using concrete models.
  • I can use strategies based on place value to divide decimals.
  • I can explain my thinking in writing when dividing decimals.
Word Problem Generator

Topic 3 - Multiply Fractions (5 days)
  • I can multiply whole numbers and fractions using models or drawings and strategies.
  • I can find the product of a whole number or mixed number and a fraction.
  • I can explain that multiplying a whole number by a fraction will result in a product that is smaller than the original whole number.
  • I can explain that multiplying a whole number by a mixed number will result in a product that is larger than the original whole number.
Preparation for fraction multiplication 
  • ​Illustrative Mathematics: Cornbread Fundraiser problem
​Multiplying Fractions by Whole Numbers activity 
​
Running a Race
Word Problem Generator

Topic 4 - Dividing Using Unit Fractions      (5 days)
  • I can interpret and compute the quotient of a unit fraction divided by a whole number and a whole number divided by a unit fraction.
  • I can use a visual fraction model to show the quotient of a unit fraction divided by a whole number and a whole number divided by a unit fraction.
  • I can use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.
  • I can use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.
  • I can create story contexts for a unit fraction divided by a whole number and for a whole number divided by a unit fraction.
  • I can solve real world problems involving division of unit fractions and non-zero whole numbers.
Dividing Fractions Video

Modeling Division of Fractions Video

Illustrative Mathematics-Converting Fractions of a Unit into a Smaller Unit
Word Problem Generator

Assessment

Unit 5 Pre Assessment
Unit 5 Real World Experience
Unit 5 Post Assessment
Formative Assessment
  • 5.NBT.B.7
  • 5.NF.B.3
  • 5.NF.B.4
  • 5.NF.B.5
  • 5.NF.B.6
  • ​5.NF.B.7



























Unit Resources

Unit Vocabulary
5th grade vocabulary cards A-L     Spanish
5th grade vocabulary cards M-Z​    Spanish
5th grade CCSS Word List (ENG-SPAN)

​ISBE Unit 3
ISBE Unit 4

Illinois TEACH & TALK 5.NBT.7
Illinois TEACH & TALK 5.NF.4
Illinois TEACH & TALK 5.NF.5
Illinois TEACH & TALK 5.NF.6

EngageNY module 1  (PDF)           (WORD)
EngageNY module 2  (PDF)           (WORD)
EngageNY module 4  (PDF)           (WORD)

Howard County Resources for 5.NBT.B.7
Howard County Resources for 5.NF.B.6
Howard County Resources for 5.NF.B.7
​
Georgia unit 4           
Georgia unit 3
​
EngageNY Lesson(partial quotients)

PARCC Sample for NF.4b
PARCC Sample for NF.2 & NF.4a
Developing Number and Operation Sense
Houghton Mifflin Textbook 310-311
Houghton Mifflin Textbook 320-321

District 5th grade Fluency Resources
​

addition flashcards: 
​(vertical)          (horizontal)          (triangle)
subtraction flashcards:
​(vertical)          (horizontal)          (triangle)
multiplication flashcards:
(vertical)          (horizontal)          (triangle)
division flashcards:
(vertical)          (horizontal)          (triangle)

Learn the Math

Fluency Assessment Directions
​Quarterly Fluency Expectations
Common Core Math Fluency Guidelines

Georgia 5th grade Overview

Parent Letter

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