Mathematics Alignment Lesson Grade 5 Quarter 3 Day 101 Common Core State Standard(s) 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 + ½ = 3/7,by observing that 3/7 < 1/2. Standards for Mathematical Practice Standard 2- Reason abstractly and quantitatively. Materials Needed: Transparencies/Blackline Masters- Strategies for Estimating with Fractions & Mixed Numbers, Blackline Master- Estimate Sums & Differences (Fractions & Mixed Numbers) Assessment Ask students How did you determine your estimated answer? (Focus on the number sense communicated in their answer.) Alignment Lesson Estimate & Round Fractions and Mixed Numbers 1. Review strategies for rounding fractions to estimate solutions using Transparency Strategies for Estimating with Fractions & Mixed Numbers. Read aloud the fractions from the answer key for this page (in random order) and have students place in the appropriate column. Then briefly discuss what the fractions in each column have in common (see answer key). (If students are struggling with understanding which fractions would fall under each benchmark have them create and compare the fractions using a manipulative such as fraction strips). 2. Ask students how they could use these benchmarks to round fractions and estimate answers. Ask how they could extend these benchmarks to round mixed numbers and estimate answers. Also have students discuss other strategies they could use to round and estimate. 3. Display Transparency Estimate Sums & Differences (Fractions & Mixed Numbers) and review the directions with students. You may want to do the first problem as an example. Once students have completed each problem, use math talk to discuss the answer to each part. Allow discuss of various strategies used to round the fractions. As students share their actual answer, make sure they explain how the estimate helps them know that the answer is reasonable. 4. Have students complete Blackline Master, Estimate the Sum for homework. Homework Blackline Master, Estimate the Sum Source: Teacher Created and Adapted from DPI Unpacking Document Vocabulary Benchmarks- Numbers convenient for comparing and ordering numbers, e.g., 0, 1/2, 1 are convenient benchmarks for comparing and ordering fractions.
Transparency/Blackline Master Grade 5 Day 101 Standard 5.NF.2 Strategies for Estimating with Fractions & Mixed Numbers 1. Fraction Benchmarks Place the fraction or mixed number your teacher reads aloud in the appropriate column. What do the fractions in each column have in common? Equal to 0 Equal to ½ Equal to 1 Fractions Much Greater Than 1 2. How can you use these benchmarks to estimate and round fractions when adding and subtracting? 3. How can you extend these benchmarks to estimate and round mixed numbers when adding and subtracting? 4. What other strategies could you use to estimate and round fractions and mixed numbers when adding and subtracting?
Answer Key Grade 5 Day 101 Standard 5.NF.2 Strategies for Estimating with Fractions & Mixed Numbers Answer Key 1. Fraction Benchmarks Equal to 0 0/8 2/12 1/8 3/20 1/10 0/12 1/9 Equal to ½ 3/8 4/8 2/4 7/12 4/10 60/100 11/20 Equal to 1 5/6 8/8 9/8 10/12 11/12 14/15 103/100 Fractions Much Greater Than 1 2 1/12 4 1/3 1 7/10 3 2/6 40/20 17/10 25/12 The numerators are much smaller than the denominators. The numerators are about half the denominators. The numerators are almost the same as the denominators. There is a whole number and a fraction or the numerator is much greater than the denominator. 2. How can you use these benchmarks to estimate and round fractions when adding and subtracting? You can look at the fractions that you need to add or subtract and determine which benchmark it is closest to and use the benchmark fraction to estimate the sum or difference. 3. How can you extend these benchmarks to estimate and round mixed numbers when adding and subtracting? You can ignore the whole number when you first look at the mixed numbers and use the benchmarks to determine if the fraction part of the mixed number is closer to 0, 1/2, 1 or greater than 1. Then use that benchmark fraction along with the whole number to find the sum or difference. 4. What other strategies could you use to estimate and round fractions and mixed numbers when adding and subtracting? You could use (or visualize) number lines. You could also use (or visualize) pattern blocks or fraction tiles.
Blackline Master Grade 5 Day 101 Standard 5.NF.2 Estimate Sums & Differences (Fractions & Mixed Numbers) Directions: Estimate the sum or difference. Explain how you rounded each fraction or mixed number to make your estimate. Find the actual answer to check to see that your estimate is reasonable. 1. 1/7 + 1/3 2. 2/3-3/5 3. 2 1/3-1/2
4. 4 12/17-1 1/7 Blackline Master Grade 5 Day 101 Standard 5.NF.2 5. 2 4/9 + 8 2/11 6. 21/8 + 3/16
Answer Key Grade 5 Day 101 Standard 5.NF.2 Estimate Sums & Differences (Fractions & Mixed Numbers) Answer Key Directions: Estimate the sum or difference. Explain how you rounded each fraction or mixed number to make your estimate. Find the actual answer to check to see that your estimate is reasonable. 1. 1/7 + 1/3 0 + ½ = ½ Using benchmarks, I know that 1/7 is close to 0 since 1 (the numerator) is much smaller than 7 (the denominator). I know 1/3 is close to ½. This is because 1 is close to half of the denominator (3). Also, if I picture a number line, 1/3 is closer to ½ than it is to 0. So, 0 + ½ = ½. 10/21 2. 2/3-3/5 ½ - ½ = 0 Using benchmarks, I know that 2/3 is close to ½. This is because 2 is close to half of the denominator (3) half of 3 is 1.5 and 2 is closer to 1.5 than it is to 0 or 3. I know that 3/5 is close to ½ because 3 is close to half of the denominator (5) half of 5 is 2.5 and 3 is closer to 2.5 than it is to 0 or 5. So, ½ - ½ = 0. 1/15 3. 2 1/3-3/6 2 ½ - ½ = 2 Using benchmarks, I know that 2 1/3 is close to 2 ½. To figure this out, I first ignored the whole number and just decided what benchmark 1/3 is close to. 1/3 is close to ½ because 1 is close to half of the denominator (3). 3/6 is 1/2 so 2 ½ - ½ = 2. 1 5/6 4. 4 12/14-1 1/7 5 1 = 4 Using benchmarks, I know that 4 12/14 is close to 5 because 12/14 is close to 1 and 4 +1 = 5. 1 1/7 is close to 1 because 1/7 is close to 0 and 1 + 0 =1. So 5 1 = 4. 3 5/7 5. 2 4/9 + 8 2/11 2 ½ + 8 = 10 ½ Using benchmarks, I know that 2 4/9 is close to 2 ½ because 4/9 is close to ½ since 4 is close to half of the denominator (9). 8 2/11 is close to 8 because 2/11 is close to 0 and 8 + 0 = 8. I know 2/11 is close to 0 since 2 is much smaller than 11 (the denominator). 10 62/99 6. 21/8 + 3/16 2 ½ + 0 = 2 ½ Using benchmarks, I know that 21/8 is much greater than 1. I know it is great than 2, but less than 3 because 16/8 would be 2 and 24/8 would be 3. 21/8 16/8 = 5/8 and 5/8 is close to ½ so 21/8 is close to 2 ½. I know 3/16 is close to 0 because the numerator is much smaller than the denominator. 2 13/16
Blackline Master Grade 5 Day 101 Standard 5.NF.2 Name: Date: Estimate the Sum Journal Prompt Is 2/5 + 1/2 = 3/7? Explain two ways to explain whether this statement is true or not using benchmarks. Adapted from DPI Unpacking Document
Asnwer Key Grade 5 Day 101 Standard 5.NF.2 Name: Date: Estimate the Sum Journal Prompt Answer Key Is 2/5 + 1/2 = 3/7? Explain two ways to explain whether this statement is true or not using benchmarks. 2/5 + 1/2 is not equal to 3/7. One way to use benchmarks to prove this is by looking first at 2/5. 2/5 is close to 1/2. 1/2 + 1/2 = 1 and 3/7 is not close to or equal to 1. Also, 3/7 is less than 1/2 (because 3 is half of 6). The solution (3/7) can t be smaller than one of the addends (1/2). Adapted from DPI Unpacking Document