LESSON PLANS
• Project the problem in the box below. Ask: How you would explain the division steps you see? Think to yourself, then explain to a partner.
Pluto: King of Dwarfs DIVISION RELATIONSHIPS PAGE 10
Estimates with Unit Form 176.9 ÷ 29 =
Solution 29 176.9 6.1 29 176.9
180 ones ÷ 30 = 6 ones 30 tenths ÷ 30 = 1 tenth
−174 ones 29
−29 tenths 0
• Now, discuss what you observe about the left side of this solving strategy compared with the right side. (The left side uses estimation and unit form while the right side uses precise calculations and the division algorithm.) • Why did the student take 176.9 and estimate it to 180 ones? Where do you see the ones in the algorithm? ( 180 ones ÷ 30 = 6 ones. Using this answer, the student plugged 6 ones into the algorithm. 6 ones × 29 = 174 ones. This leaves 2 ones and 9 tenths, or 29 tenths. ) • In the second estimate, why is the student is estimating by tenths? Where do you see the tenths in the algorithm? ( 30 tenths ÷ 30 = 1 tenth. The student then placed 1 tenth in the algorithm. 29 tenths × 1 = 29 tenths, leaving a difference of 0. ) • Does our answer make sense? Where did the student decompose the numbers to make solving simpler? (176.9 was decomposed into 180 ones, so that you could evenly divide without regrouping. 29 groups was also rounded to 30 groups.) • Discuss what the standard form of 29 tenths looks like. (2.9) Do you see this in the algorithm? (No, you see 29 tenths.) Application 3. Have students solve the article’s problems. Continually question them so they make connections between estimation/unit form and the standard algorithm. These connections take time and practice. Closure 4. Give students further practice with the “Division Relationships” skills sheet.
CONTENT STANDARD Numbers & Operations in Base 10:
OBJECTIVE Students will deepen their understanding of division using estimation, precise place value vocabulary, and the standard algorithm. OPTIONAL MATERIALS whiteboards and markers LESSON Engagement 1. Before reading the article, ask questions and facilitate discussion either as a whole group, in small groups, or with a partner: • How many of you have heard of a dwarf planet? Discuss what you think one is. • There are dwarf planets throughout our solar system. What do you think scientists use to study them? Concept Development 2. After reading, ask questions and facilitate discussion with the following questions: • When solving division problems, what other operations or strategies could you use to help you find your answer? (possible responses include: multiplication, repeated addition, skip counting) • Have you ever solved division problems using unit form vocabulary? Discuss how using precise unit form vocabulary can help you solve these problems. Perform division with multi-digit whole numbers and decimals, using the inverse relationship with multiplication. MATHEMATICAL PRACTICES STANDARDS 2. Reason abstractly and quantitatively. 6. Attend to precision. 8. Look for and express regularity in repeated reasoning.
DYNAMATH TEACHER’S GUIDE T5
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