Day 1 – Fractions as Quotients (Equal-­‐Sharing) Goals: I can solve an equal sharing problem by drawing pictures and reasoning with numbers. I can write an equal sharing word problem for my students to solve and predict a range of strategies that they will use to solve the problem. I can modify the numbers in an equal sharing problem to differentiate instruction. I can use questioning to encourage children to use more sophisticated sharing strategies. Which thing does not belong? 𝟏 𝟏
+ 𝟐 𝟒
𝟏 𝟏
+ 𝟐 𝟔
𝟏 𝟏
+ 𝟑 𝟑
𝟐
𝟑
Equal Sharing Problem 4 children share 7 cookies evenly. How much of a cookie does each child receive? Five Practices for Orchestrating Productive Mathematical Discussions 1. 2. 3. 4. 5. Anticipate Monitor Select Sequence Connect Day 1 – Fractions as Quotients page 2 Equal Sharing Problems Solve each of the problems below by drawing pictures to show your thinking. A. Kyle and Derek have 23 cookies. If B. There is one and three-­‐fourths cups they share the cookies evenly, how of lime-­‐aid in the refrigerator. Mike many cookies will each person get? and Karla want to share the lime-­‐
aid equally. How much lime-­‐aid will each person get? C. Brooke purchased 11 burritos at D. Three people share two apple pies Chipotle. She and her three equally. How much of a pie will brothers plan to eat them all and each person receive? share them equally. How much will each person get? Day 1 – Fractions as Quotients page 3 E. There are 17 pounds of birdseed in F. Four pirates want to share 24 coins a large can. Rimma wants to put evenly. How many coins will each the birdseed into three containers pirate receive? with the same amount in each container. How many pounds of birdseed will be in each container? G. Four friends want to share three quarts of ice cream evenly. How much ice cream does each friend receive? H. Amanda has a ribbon that is 9 meters long. She wants to make 12 headbands of equal length. How long will each headband be? Day 1 – Fractions as Quotients page 4 Multiplication and Division (Draw a picture) A. B. C. Day 1 – Fractions as Quotients page 5 Problem Type A. Multiplication (repeated addition) Marlo gives five pieces of candy to each of her four friends. How much candy does she give away? B. Measurement Division (repeated subtraction) Jay has 15 cups of flour. Each batch of pancakes he makes requires three cups of flour. How many batches can he make? C. Partitive Division (equal sharing) Four pirates want to share 24 coins evenly. How many coins will each pirate receive? # of groups amount in each group total equation Ways for kids to make sense of number sentences expression in words Multiplication Sentence Measurement Division (repeated subtraction) Partitive Division (equal sharing) Day 1 – Fractions as Quotients page 6 A. Write your own equal sharing (partitive division) problem for 𝟏𝟑 ÷ 𝟒 (4 sharing 13) B. Write your own equal sharing problem for 𝟓 ÷ 𝟖 (___ sharing ___) Day 1 – Fractions as Quotients page 7 C. Write your own equal sharing problem for 𝟒 ÷ 𝟔 (6 sharing 4) Day 1 – Fractions as Quotients page 8 Analyzing Student Work Problem: Six children share four candy bars evenly. How much candy bar can each child have? A B C D E F Day 1 – Fractions as Quotients page 9 Types of strategies children use to solve Equal Sharing Problems (page 25 of Extending Children’s Mathematics) children share four candy bars evenly. How much candy bar can Problem: Six each child have? Strategy Name Non-­‐Anticipatory Sharing Strategy Description Additive Coordination – Sharing one item at a time Additive Coordination – Sharing groups of items Ratio -­‐ Repeated halving -­‐ Factors Multiplicative Coordination Day 1 – Fractions as Quotients page 10 Predict Student Responses Problem: Paul and Joe want to share 7 cookies evenly. How many cookies would each person receive? strategy non-­‐equal groups picture do not use up all being shared non-­‐anticipatory sharing (correct) additive coordination ratio or factor multiplicative coordination Day 1 – Fractions as Quotients page 11 Problem: There are five cups of juice on the table. Eight children want to share the juice equally. How much of a cup of juice should each child get? strategy non-­‐equal groups picture do not use up all being shared non-­‐anticipatory sharing (correct) additive coordination ratio or factor multiplicative coordination Day 1 – Fractions as Quotients page 12 Problem: _______ children share ______ burritos equally. How many burritos does each child receive? (4,5) (6,10) (12,16) strategy non-­‐equal groups picture for (4,5) picture for (6,10) picture for (12,16) do not use up all being shared non-­‐
anticipatory sharing (correct) additive coordination ratio or factor multiplicative coordination Day 1 – Fractions as Quotients page 13 Day 1 – Fractions as Quotients page 14