# PS 42X Grade 5 Unpacking Chapter 5

### Chapter 5 Divide Decimals

Released Items: 5.NBT.2 (tested every year, only 1 item released), 5.NBT.7

Data from June Instructional Report 2015:

• 5.NBT.2, MC, 83%
• 5.NBT.7, MC, 83%
• 5.NBT.7, CR, 19% achieving 2 points

Stage 4 Fluencies:

• Recognizing exponents and powers of 10 in exponential form
• Writing number, including numbers with decimals in expanded form using various forms to represent powers of 10, i.e. decimal form, decimal fractions, exponents, etc.
• Equivalent form of decimals amounts, i.e. 24 tenths is 2.4 or 2 whole ones 4 tenths
• Divide any number by 1, 1/10, 1/100

Thoughts on Lessons:

1. Tools: Place value chart, money, base ten blocks
2. Models: Open Array/Area Model
3. Strategies: sharing out, equal groups (when the divisor can be viewed as 9 groups or less), regrouping the dividend when you realize that the amount in the lead place value cannot be equally distributed given the divisor.
4. Lesson 5.1: This lesson is idea for number strings and the use of a place value chart to visualize what is happening. Would be lesson by looking at 10x more on a place value chart, then dividing.  Would not emphasize the problems with multiplying or dividing by thousandths. Standard says, “Add, subtract, multiply and divide decimals to hundredths…”  Would use the Reteach and Enrichment sheets for student work. Would look at the Advanced Learners and adapt idea for lesson and make a matching game or a “Which does not belong?”
5. Lesson 5.2: Book provides took much scaffolding. Present problems, but have students determine what to do and why. Revise lesson by giving a problem situation and teaching students how to solve. Rework the problem and use a Rally Coach strategy to have students collaborate to solve. Use of concrete models is key as called for by the standards. Instead of just doing the workbook problems on page 299, why not have the problems on index cards and have the student solve using Rally Coach using concrete and pictorial models using either an equal groups or sharing out strategy.
6. Lesson 5.3: Do a as quick daily routine, but do not teach this entire lesson. Use problems from lessons, but do as part of a routine one at a time. Could make into a center game…look at the Advanced Learners.
7. Lesson 5.4: Use a sharing out when the divisor is greater than 10. Use an equal groups when the divisor can be viewed as 9 groups or less. Show student how to recognize when regrouping the dividend is going to be necessary. Also, select problems where the numbers are more user-friendly, can be given a context and visualizable. If doing long division, emphasis what each calculation on the dividend means. Use of partial quotients is encouraged. Use Rally Coach strategy and partner students strategically. Spend 2 days on this topic, if possible. Make into a game as much as possible, e.g. Math Tic Tac Toe.
8. Lesson 5.5: Use visual models and show students how to make quick drawings to work out problems. Focus on the sharing out strategy where you are sharing out equal groups of the divisor from the whole (dividend). Use the Advanced Learners and Enrich ideas as examples of how to adapt this lesson. Spend 2 days on this topic, if possible.
9. Lesson 5.6: It is important to provide students with the opportunity understand the concept of why this strategy works. First, begin with simpler, more user-friendly numbers. For example, 10 divided by 2 is 5. Not multiply the dividend by 10, will produce 100. Multiply the divisor by 10 will produce 20. So our new problem is 100/20 and the quotient is still 5. This is because we are creating equivalent fractions and division is just another representation of fractional amounts and what we have done is multiply 10/2 by 10/10 or by 1 whole to create an equivalent fraction of 100/20.
10. Lesson 5.7: This lesson is really about not have a remainder. Only work with the problems whose quotient ends in the tenth or hundredth places. Make all the problems about money. Either avoid the problems where students might need to create an equivalent fraction as taught in lesson 5.6 or have students recognize which problems are easier solved my making equivalencies. Focus on the problems where equivalencies are not needed. For example, page 331 #1, – 7, 9, 10, etc. However, look at all the problems carefully and use money and/or base-ten blocks to visualize. For example, page 331 #11 is 2.43/0.54 could be asking, “If I had \$2.43, how many groups of \$0.54 (read 54 cents) can I make?” Or I could ask, “”If I had \$2.43, how many times could I share out \$0.54 (read 54 cents)?”
11. Lesson 5.8: Adapt and infuse problems all throughout the unit and provide time for student to work out. Could be a word problem of the week.