Thinking Flexibly About Numbers

1. Thinking Flexibly About Numbers Unit of Study1: Place Value Concepts Global Concept Guide: 3 of 3

2. Content Development • This GCG is critical in building the foundation for regrouping in 2nd grade and in future grade levels. • Learning tasks should be designed to build understanding that different representations of a number have the same value. For example, 3 tens and 2 ones has the same value as 2 tens and 12 ones, 1 ten and 22 ones and 0 tens and 32 ones. • All students need to use base ten blocks the first two days and many students will still need to use them for Days 3 and 4. • For more information on teaching this GCG please see Modeling a Number in Different Ways Go Math! TE p. 33A.

3. Day 1 • Essential Question: How can you use base ten blocks and quick pictures to model the value of a number in different ways? • Provide each student with base ten blocks to use when solving the following problem: Danny has 23 pencils. He used the base ten blocks shown to model the number of pencils he has (display two rods and three units). How can you create a different model to represent Danny’s pencils? • While students are solving, look for a child who trades one or more of the rods for units to highlight in sharing session. • Facilitate discussion of multiple representations of one value. • Use the above problem as a reference for creating more problems (along with problem solving scenarios from Lesson 1.6) allowing students the opportunity to use base ten blocks to model numbers. Students should be able to compose and decompose numbers in order to flexibly represent values. • Once the majority of students demonstrate an understanding of flexible representation with manipulatives, introduce quick pictures. • By the end of day 1, students should be able to use manipulatives or quick pics to represent numbers.

4. Day 2 . . . . . • Essential Question: How can you solve problems involving representing numbers flexibly? • Provide each student with base ten blocks to use when solving the following problem: Which girl above has the most bracelets? Which girls have the same number of bracelets? How do you know? Draw a quick picture to show the number of bracelets _____ has. Use base ten blocks to represent _____’s number of bracelets in another way. • Use teacher observations from Day 1 along with student performance on engage task to assign small group reteach or problem solving task fromWord problems for representing numbers flexibly. • Encourage students to use direct modeling with base ten blocks to make sense of problems. • By the end of Day 2, students should be able to use base ten blocks to represent a given value multiple ways. Students should be able to create quick pictures to represent their models.

5. Day 3 • Essential Question: How can you organize and record your flexible representations of numbers? • Engage: Jana is trying to represent 46 in all of the ways possible. Look at her work below to see the combinations she has come up with so far: 4 tens 6 ones, 0 tens 46 ones and 3 tens and 16 ones. How can you organize Jana’s work to see if she has found all of the representations? • Look for opportunities to have students share the most efficient strategies for organizing information. • Provide additional problems with SE. p 37, Unlock the Problem. • Use Lesson 1.7 over Days 3 and 4 to pull student tasks. • Sample lesson closure journal activity: What are all the ways to represent the number 74? • By the end of day 3, students should be able to represent numbers in a variety of ways and use a strategy to ensure they have recorded all the different representations.

6. Day 4 • Essential Question: How does finding a pattern help you find all the ways to show a number? • Engage: Grandma’s purse has dimes and pennies. She has 52 cents. What are all of the possible combinations of coins in Grandma’s purse? • Once students can organize their representations into a chart or graphic organizer, the focus for Day 4 should be spent on looking for patterns to ensure all possible flexible representations are included. • Day 4 could also be used to pull a small group of students who are struggling with organizing information into a graphic organizer. • Ask HOT questions to elicit discussion on looking for patterns to ensure all possible representations are included in student charts. • Sample lesson closure journal activity: How can you prove you have all of the possible representations of 87? • By the end of day 4, students should be able to represent numbers in a variety of ways and use a strategy to ensure they have recorded all the different representationsof those numbers.

7. Enrich/Reteach/Intervention Reteach • The Tier 2 intervention lesson idea from Go Math TE p. 33B could be used with a small group who needs explicit reteaching. • Reteach Animated Math Model Flexible Representation • Use TE p. 35 Math Talk in Action to support small group discussion. Enrich • The Enrich ideas from Go Math TE p. 33B & 37B would be good to extend students thinking. • The “What Number Am I?” riddle cards can be played with students who are fluent in representing numbers flexibly.