Unit of Study 1: Place Value Concepts Global Concept Guide 2 of 3

Content Development “Physical models for base-ten concepts can play a key role in helping children develop the idea of “a ten” as both a single entity and as a set of ten units. Remember though, that the models do not “show” the concept to the children. The children must mentally construct the concept and impose it on the model” (Van de Walle, 2010) Initially, rather than using standard number words, more explicit base-ten language, can be used. In base-ten language, rather than saying “forty-seven” you would say “four tens and seven ones.” (Van de Walle, 2010) Students should spend the majority of their time using tools or drawing quick pics to flexibly represent the value of the number. Students should understand the different forms of numbers: standard, expanded, word, and base ten. For more information on teaching place value, click here.

Day 1 Essential Question: How can you determine the value of a digit depending on its place in a number? Have base ten blocks available for students to use when solving the Listen and Draw question on p. 21 in Go Math: Lesson 1.3. After students build the model, have them draw a quick pic of the model. Students should be able to connect their models and pictures with the number in expanded form. To build students’ conceptual understanding through problem solving, use Go Math SE p.24 and/or use similar problem solving scenarios such as: Jennifer rolled two number cubes. The first cube landed on four, and the second cube landed on one. What are the two different two-digit numbers Jennifer could have? Build or draw a model that supports your thinking. Example Journal Question: Explain how you know the values of the digits in the number 58. By the end of Day 1, students should be able to build and/or draw representations of 2-digit numbers. They should also understand how the value of a number changes depending on the order of the digits.

Day 2 Essential Question: What are different ways to represent a 2-digit number? Lessons 1.4 and 1.5 will be combined to connect the models and/or quick pics to expanded form, word form, standard form and base ten. Children will continue to build their understanding of composing and decomposing numbers with base ten blocks, quick pictures and expanded form. Teachers’ questioning on Day 2 should focus on making connections between the different representations of numbers. Example Engage: Place a two-digit number, such as 27, on the board. Challenge students to build or draw a quick pic representing the number with the fewest blocks possible. Refer to page SE p. 26 and 27 for additional examples. Have base ten blocks, secret code cards, number cubes, hundreds boards, place value charts etc., available for students to use when solving problems from Lessons 1.4 and 1.5. Select questions from pages 30-31 , challenge students to represent the number two different ways.

Day 2 Continued… Essential Question: What are different ways to represent a 2-digit number? Utilize the Problem Solving Page SE p.28 to apply understanding of various ways to represent numbers. By the end of Day 2, students should be able to build and/or draw flexible representations of 2-digit numbers and record those representations in different ways: standard, expanded, word, and base ten. In order to assess this, use the following or a similar scenario: PERFORMANCE TASK: Represent the number 63 in four different ways. Explain if 63 is an even or odd number. Successful students will be able to represent the number in standard form, word form, expanded form, and base ten language.

Enrich/Reteach/Intervention Struggling students should be given more time to build numbers with base ten blocks. Provide opportunities to create numbers using base ten blocks, and connect the base ten blocks to expanded form. Use the non-fiction book Whales (SE p. 1-8) as a way to reteach or extend building and representing numbers. Go Math Animated Model: Understand Place Value -Focuses on tens and ones and the value of digits. Go Math Animated Model: Tens and Ones- Focuses on tens and ones and the value of digits. Go Math Animated Model: Read and Write Numbers- Focuses on different ways to represent two digit numbers Enrich The enrich lesson ideas from Lessons 1.3-1.5 (p. E3-5, TE p. 29B) would be appropriate ways to extend students’ thinking within this concept. Provide number riddles to students Example: I have 23 ones and 4 tens. Who am I? Example: If you put 3 more tens with me, I would be 85. Who am I?