After they have had some time to work on these problems, ask several students to share their solutions for Questions 2–3 on the Estimate Fraction Sums with Number Lines pages in the Student Activity Book.
- What strategy did you use to solve Question 2? (Possible response: I know that 1/3 = 2/6, so 2/3 will equal 4/6. 4/6 + 1/6 = 5/6 and that is less than 1, so Maya walked less than a mile.)
- How can you show this using one of the number lines? (Possible response: I can add sixths to the number line that is divided into thirds. 1/6 will be halfway between zero and 1/3, 1/3 and 2/6 are the same mark, 3/6 is halfway between 0 and 1; 4/6 and 2/3 are the same mark, 5/6 will be halfway between 2/3 and 1, and finally 6/6 is the same mark as 1. On the number line you can see that 5/6 is less than 1.)
- How can you show the solution for Question 2 using circle pieces? (Possible response: Two orange pieces equals 2/3. One aqua piece is equal to 1/6. When you put 2 orange pieces and 1 aqua piece together it will not fill the whole red circle. So Maya walked less than 1 mile.)
- How did you solve Question 3? (Possible response: 1/6 is smaller than 1/4. Since it takes 2/4 to equal 1/2, 1/4 + 1/6 will be less than 1/2.)
- How do you know that 1/6 is less than 1/4 ? (Possible response: When two fractions have the same numerator, you can compare them using the denominator. The smaller the denominator the larger the fraction because when the whole is divided into fewer pieces, each piece will be larger.)
- If Keenya divided her candy bar into 12 equal parts, and ate 1/6 of the candy bar on Wednesday, how many of the 12 pieces did she eat? (2) How did you decide? (Possible response: I know that 1/6 = 2/12 , so if Keenya ate 1/6 of the bar she ate 2 of the 12 pieces.)
- How many pieces of the bar did Keenya eat when she ate 1/4 of the bar? (3 pieces) How did you decide? (Possible response: Since 1/4 = 3/12 , when Keenya ate 1/4 of the bar she ate 3 of the 12 pieces.)
- If Keenya ate 2 pieces of the bar on Wednesday and 3 pieces on Thursday, what fraction of the bar did she eat in all? ( 5/12 )
- How can you use these different strategies and tools to help you decide if your solutions are reasonable? (Possible response: If you solve a problem one way, for example, with circle pieces, you can check your answer by solving the problem using a different strategy. If the answers are the same you know you answer is reasonable.)
Direct students to the Kathy's Hot Chocolate section of the Estimate Fraction Sums pages in the Student Guide. Assign Check-In: Questions 8–9 for students to complete independently.
Use Check-In: Questions 8–9 on the Estimate Fraction Sums pages in the Student Guide to assess students' abilities to use benchmark fractions to estimate sums and assess reasonableness of answers [E9].
Ask a student to check the answer to Question 8 using water and 1-cup, 1/3 -cup, and 1/4 -cup measuring cups. The student can fill the 1/3 -cup twice and the 1/4 -cup halfway to simulate making the hot chocolate.
