Curriculum Map

Adding and Subtracting Fractions and Mixed Numbers

OVERVIEW
6 Days Adding and subtracting   fractions 

 

 

 

 

 

 

 

 

  • Rewrite two fractions and or mixed numbers with unlike denominators to have common        denominators in order to add or subtract fractions.
  • Add fractions and mixed numbers both with like denominators and with unlike denominators.
  • Subtract fractions and mixed numbers both with like denominators and with unlike denominators.
  • Simplify all solutions.

 

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.)  **See Resources submitted with Unit Plan** VOCABULARY*Simplify

*common denominators

*unlike denominators

*fraction

*equivalent

*reduce

*mixed number

*improper fraction

*numerator

7 Days Fractions and real world   situations
  • Solve word problems involving addition and subtraction of fractions of like and unlike        denominators referring to the same whole.
  • Using estimation and benchmark fractions, justify the reasonableness of a fraction solution.

 

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 < 1/2.  **See Resources submitted with Unit Plan** VOCABULARY*unlike   denominators

*benchmark   fractions

*estimation

*fraction

*equivalent

*reduce

*mixed   number

*improper   fraction

 

2 Days

Review and QUIZ

Multiplying Fractions and Mixed Numbers

 OVERVIEW
1 Day Fractions
  •   Define a fraction as division of the numerator by its  denominator.
  •   Solve word problems involving the division of two whole numbers where the solution will be a fraction or a mixed number.
  •   Using a number line, explain between what two whole numbers the fraction solution lies.
5.NF.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? **See Resources submitted with Unit Plan** VOCABULARY*Numerator

*Denominator

*Division

*Quotient

3 Days Multiplying fractions and   whole numbers
  •   Draw a fraction model to illustrate a product of a fraction by a whole number and a fraction by a fraction.
  •   Relate multiplying by a fraction as taking “part of” a  whole number.
5.NF.4a. 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.) **See Resources submitted with Unit Plan** VOCABULARY*part   of

*area

*tiling

*unit   fraction

 

1 Day Area of rectangles with   fractional side lengths
  •   Find the area of a rectangle with fractional side lengths.
  •   Tile a unit square into unit fraction side lengths.
  •   Using tiling prove the equivalence of multiplication and area.
5.NF.4b. 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. **See Resources submitted with Unit Plan** VOCABULARY*Tiling

*unit   square

*equivalence

 

1 Day Size of products
  •   Describe the size of a product in terms of how many times larger one factor is to another without multiplying.
  •   Explain and show why multiplying by a fraction equal to 1 will result  in an equivalent fraction.
5.NF.5a. Comparing   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. **See Resources submitted with Unit Plan**

 

VOCABULARY*Product

*Factor

*improper   fraction

*mixed   number

 

1 Day Size of products
  •   Explain and show why multiplying by a fraction less than one will result in a product less than the greater number.
  •   Explain and show why multiplying by an improper/mixed number will result in a product greater than the given number.
  •   Rewrite the number 1 as an equivalent fraction i.e. 2/2, 3/3,   4/4, etc.
5.NF.5b. 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. **See Resources submitted with Unit Plan** VOCABULARY*Product

*Factor

*equivalent   fraction

 

1 Day Multiplying fractions and   mixed numbers
  •   Solve word problems involving multiplication of fractions and mixed numbers.
  •   Represent the product of fractions in simplest form.
  •   Write equations to represent word problems involving multiplication of fractions.
  •   Draw/show multiplication of fractions through visual models.
5.NF.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.

 

**See Resources submitted with Unit Plan** VOCABULARY*Fractions

*mixed   number

*visual   models

 

1 Day

Quiz

Dividing Fractions and Mixed Numbers

 OVERVIEW
1 Day Division of unit fractions and   whole numbers
  •   Define a unit fraction as fraction with a numerator of 1.
  •   Divide a unit fraction by a whole number.
  •   Draw/show division of a unit fraction by a whole number as dividing the unit fraction into smaller parts.
  •   Create a story in which division of a unit fraction by a whole number is used.
  •   Explain the effects of dividing a unit fraction by a whole number.
  •   Justify the reasonableness of answer in the context of a problem.
  •   Simplify/reduce quotients to lowest terms.
5.NF.7a. 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. **See Resources submitted with Unit Plan**

 

VOCABULARY*unit   fraction

*whole   number

*divide

*estimation

*quotients

*lowest   terms

 

2 Days Division of unit fractions and   whole numbers or unit fractions
  •   Define a unit fraction as a fraction with a numerator of 1.
  •   Divide a whole number by a unit fraction.
  •   Create a story in which division of a whole number by a unit fraction is used.
  •   Explain the effects of dividing a whole number by a unit fraction.
  •   Define the reciprocal of a unit fraction for the purpose of division.
  •   Simplify/reduce quotients to lowest terms.
  •   Justify the reasonableness of answer in the context of a problem.
5.NF.7b. 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. **See Resources submitted with Unit Plan**

 

VOCABULARY*unit   fraction

*whole   number

*divide

*estimation

*quotients

*lowest   terms

*numerator

*denominator

 

1 Day Division of unit fractions and   whole numbers
  •   Divide a whole number by a unit fraction (vice versa) in the context of word problems.
  •   Solve a story/word problem in which division of a whole number by a unit fraction (vice versa) is used.
  •   Explain the effects of dividing a whole number by a unit fraction (vice versa) in the context of a word problem.
  •   Justify the reasonableness of answer in terms of the context of the problem.
  •   Simplify/reduce quotients to lowest terms.
5.NF.7c.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? **See Resources submitted with Unit Plan** VOCABULARY*unit   fraction

*whole   number

*divide

*estimation

*quotients

*lowest   terms

*numerator

denominator

1 Day

Quiz

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