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BNM2 Task 4: Understanding and Teaching Fractions, Decimals, or Percentages Western Governors University August 31, 2021

2 A. 1. First Standard: Fourth Grade  CCSS.MATH.CONTENT.4.NF.B.3.B: Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model (Common Core Standards, 2021). Second Standard: Fifth Grade  CCSS.MATH.CONTENT.5.NF.A.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 (Common Core Standards, 2021). Third Standard: Sixth Grade  CCSS.MATH.CONTENT.6.NS.A.1: Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem (Common Core Standards, 2021). 2. Sample Problem: Fourth Grade  CCSS.MATH.CONTENT.4.NF.B.3.B – Decompose the following fractions into smaller fraction equations with the same denominator. Draw a picture of the fraction to show your work. o 4 5

3 o 2 7 8 Sample Problem: Fifth Grade  CCSS.MATH.CONTENT.5.NF.A.1 – Find the common denominator to solve the equations. o 3 8 + 1 2 o 4 5 - 2 3 Sample Problem: Sixth Grade  CCSS.MATH.CONTENT.6.NS.A.1– Solve the following word problem: How many 2 3 cup servings are in a 7 3 cup of sugar? 3. First Sample Problem Solution: Fourth Grade  To solve the problem, the student will first need to read the instructions and see that they are decomposing or breaking down the fractions into smaller fraction equations. To do so, they will need to look at the numerator first, as the denominator will be staying the same. For the first problem 4/5, the students could choose to do the equation 2/5 + 2/5 = 4/5, to which they would use the visual: + = showing how they broke down the fraction into smaller pieces. For the second problem 2 7/8, the students will need to break the whole number apart as well. An example answer could be 1 + 1 + 3/8 + 4/8 = 2 7/8. This answer

4 shows the student breaking apart the whole number as well as decomposing the fraction into two smaller pieces. The visual for this answer would be: + + + = Second Sample Problem Solution: Fifth Grade  First, the student will need to identify the LCD, or least common denominator in this problem. After going through a multiplication table, the student will find that the LCD for 3/8 and 1/2 is 8. To get 1/2 to have a denominator of 8, they must multiply both the top and bottom by 4 to get the fraction 4/8. The student will then add together the fractions to get the answer to the equation which is 7/8. For the second problem, the student will need to find the LCD of 4/5 and 2/3. Since 5 and 3 share 15, the student will need to multiply both fractions to get the LCD of 15. They will need to multiply both numerator and denominator of 4/5 by 3, and multiply both numerator and denominator of 2/3 by 5. They will then have the equation 12/15 – 10/15. The students will then subtract the fractions now that there is a similar denominator and arrive at the answer of 2/15. Third Sample Problem Solution: Sixth Grade  The student will first need to identify what the question is asking. They will realize that they will need to divide the cups of sugar by the serving size. This will give them the equation 7/3  2/3. To solve this equation, the students will need to turn the division problem into a multiplication problem by multiplying by the reciprocal. This will turn 7/3  2/3 into 7/3 x 3/2. Now the students will multiply the fractions straight across, giving them 7 x3/ 3x2. After solving the

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