Division Using Place Value

1. Division Using Place Value Unit of Study: Strategies for Dividing by 1-Digit Divisors Global Concept Guide: 3 of 4

2. Content Development “Students use base-ten blocks to model division. When students learn to divide, a roadblock to success can be a lack of mastery of basic division facts. Working with base-ten models not only increases a student’s mastery of basic division facts, it also forms a foundation for understanding the concept of division. When students become familiar with concrete models like base-ten blocks, they are more likely to understand concepts in such a way that real models are no longer needed.” - Go Math TE p. 171A “Students will use reasoning skills to make predictions, solve problems, and check their solutions. Guide them to see how the parts of the division algorithm are interrelated and how the operations of multiplication and division are used throughout the process. Students will need to apply previous knowledge of multiples to predict whether division problems will results in quotients with remainders. Students will also recognize when a zero should be placed in a quotient. It is important that students understand the inverse relationship between multiplication and division to check their solutions.” - Go Math TE p. 179A By the end of this GCG, “Students will have used different strategies to divide by 1-digit divisors with up to 4-digit dividends. The goal is to have students summarize and apply the strategy that is most efficient for them to use to divide.” - Go Math TE p. 181

3. Abandon or Delay Traditional Algorithms “Far too many students learn them [traditional algorithms] as meaningless procedures, develop error patterns, and require an excessive amount of re-teaching or remediation. If you are going to teach the traditional algorithms, you are well advised to spend a significant amount of time with invented methods. Delay! The understanding that children gain from working with invented strategies will make it much easier for you to teach the traditional methods.” -Van de Walle

4. Day 1 • Essential Question: How can you use base-ten blocks to model division with re-grouping? • Prior to Day 1’s Lesson, give the Traveling Circus performance task. Use the results of the performance task to make instructional decisions and make connections to future content to continue review as needed. This performance task should not exceed 30 minutes. • Engage students with the “Investigate” problem TE p. 171. Students should model the process of division with base ten blocks. Then have students draw a quick picture of their base-ten model. Encourage students to move to just using the quick picture. Have students practice problems on SE p. 173 #1-5 with a partner. Students should justify their model to their partner using place value vocabulary. • At this point, students should be focused on conceptual understanding of division, not recording the steps of the traditional algorithm.

5. Day 2 • Essential Question: How can you record division with re-grouping? • Engage students with the problem Go Math TE p. 176 “Example 2.” Students should represent the division problem with base-ten blocks or quick pictures. While a student is sharing how they created their model, the teacher should model how to record the traditional algorithm. • Use TE p. 175 “Unlock the Problem.” Have students continue modeling the problem with base-ten blocks and recording the traditional algorithm. Facilitate a group discussion about how students decided where to place the first digit of the quotient. • Use select problems from 4.10 to continue to build conceptual understanding of the traditional algorithm. Students should make connections to how place value helped them place the first digit. • Evidence of Learning • Pose problem p. 177 #7 to have students solve in their journal with a quick picture and record the traditional algorithm.

6. Day 3 • Essential Question: How can you use place value to determine the quotient? • Engage students by placing the Place the First Digit sorting cards into piles based on where the first digit of the quotient will be placed. This will be a strategy students need to continue throughout place value division. Have students justify their thinking. • Use problems as referenced on the GCG from Go Math Lesson 4.11 & Go Math Lesson 4.12 (focus on the problems not the bar model). The goal is for students to become more efficient using the traditional algorithm. • By the end of Day 3, students should be able to compare and contrast partial quotients and place value strategies for division. Students should also use inverse operations to check their solution. • If time in Day 3, see next slide with suggested differentiated division activities. • Evidence of learning • Pose problem p. 182 #18

7. Enrich/Re-teach/Intervention • Re-teach • Animated Math Models skill 17, skill 18, skill 19 • Re-teach pages: R36, R37, R38, R39 • Core • Divide and Conquer (Grab & Go) – extra practice with division strategies • Animated Math Models skill 17, skill 18, skill 19 • MegaMath Up, Up, and Array Level O, Level P • Destination math tutorial introduction to long division • Enrich • Division Drying (E36) – practice division with 1-digit divisors • How Many Digits (E37) – decide how many digits will be in the quotient • It’s A Riddle (E39) – division problem solving