Chapter 4 Multiplying Decimals
- Dr. X’s Amazing multiplication contraption
- 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
- Use the “Review” questions for centers and problem solving tasks on a daily basis. Rework these problems.
- Review this problem:
- On Saturday, Ahmed walks his dog 0.7 mile. On the same day, Latisha walks her dog 0.4 times as far as Ahmed walks his dog. How far does Latisha walk her dog on Saturday?
- Joaquin lives 0.3 mile from Keith. Layla lives 0.4 times as far from Keith as Joaquin. How far does Layla live from Keith? Write an equation to solve.
- Brianna is getting materials for a chemistry experiment. Her teacher gives her a container that has 0.15 liter of a liquid in it. Brianna needs to use 0.4 of this liquid for the experiment. How much liquid will Brianna use?
- “Review” section, pg. 287 – 288. What are the misconceptions?
- Make a simple problem as a strategy and make a visual.
Thoughts on Lessons:
- Tools: Place value chart, money
- Models: Open Array/Area Model
- Strategies: Distributive Property of Multiplication
- POD worth doing (4.1, 4.2) mentally and visualizing for a quick review and as a way to help students discuss what they know, what the numbers means given the context and what the solution means. Can do some for HW.
- Lesson 4.1: Need to model the pattern! Use the “Enrich” ideas on Day 1 and then the “Reteach” ideas on Day 2…not the lesson proposed. Can do activity, “Find Someone Who” is next in my sequence. For example, 4 x 10, 4 x 1, 4 x 0.1, etc. and explain the relationships. Students should use a place value chart to organize their thinking and to support the use of mathematically precise language. If you are going to follow the lesson, read the problems carefully and use comprehension strategies. You cannot with conceptual understanding and reading comprehension of the context do all three problems at the beginning of this lesson. It is advisable to begin with the “Problem Solving Application” at the end of the lesson and model that. If you do, then you are just focusing on a procedure, not the instructional shift of application!
- On page 234, “Try This” this is an opportunity for a Number String.
- On page 254, “Go Deeper” is a good problem for a small group to tackle together. The “Think Smarter” is going to turn into a procedure, unless their is an opportunity to discuss the patterns noted.
- Lesson 4.2: C-R-A. Model first! Present the story, visualize and model concretely. Focus on the groups of things and always give a context. For example, 8 x 0.25. I had 8 quarters in my pocket. Turn activities 1 – 3 on page 241 into a center. Students could take a blank hundred grid to represent the hundredths for work out a problem like 4 x 0.12 visually. Then they could do a Quiz, Quiz Trade activity. Also use money here, then model on grid. Jump to the “Problem Solving Application” on pg. 242
- Make a mathematical sketch: Carrie has 0.73 liter of juice in her pitcher. Sanji’s pitcher has 2 times as much juice as Carrie’s pitcher. Lee’s pitcher has 4 times as much juice as Carrie’s pitcher. Sanji and Lee pour all their juice into a large bowl. How much juice is in the bowl? (pg, 241) Use graphic organizer.
- Look at problem 11 on pg. 242…what concept is being applied. Does the model actually match the original equation?
- Lesson 4.3: COMBINE WITH LESSON 4.4 and do ideas in 4.4 first!!! Model this using the Open Array/Area Model! Model CONCRETELY!! They also mention using partial products, but they do not show the amounts using expanded form. You need to use expanded form. Make anchor charts for reference. Show both ways side by side. Make the Problem Solving Application in a real event and have students work it out. Can be a Guided Math Group as real money is required.
- Lesson 4.5: Ideas of money should be infused all during the year. Apply C-R-A with concrete materials, math models and equations. Make sure you use reading comprehension strategies to unpack the problems. “Advanced Learners” problem can be used in a Guided Group.
- Lesson 4.6: Quote from the NBT K – 5 Progression, pg. 19:
“General methods used for computing products of whole numbers extend to products of decimals. Because the expectations for decimals are limited to thousandths and expectations for factors are limited to hundredths at this grade level, students will multiply tenths with tenths and tenths with hundredths, but they need not multiply hundredths with hundredths. Before students consider decimal multiplication more generally, they can study the effect of multiplying by 0.1 and by 0.01 to explain why the product is ten or a hundred times as small as the multiplicand (moves one or two places to the right). They can then extend their reasoning to multipliers that are single-digit multiples of 0.1 and 0.01 (e.g., 0.2 and 0.02, etc.).”
- Page 267, Rachel buys 1.5 pounds of grapes. She eats 0.3 of that amount on Tuesday and 0.2 of that amount on Wednesday. How many pounds of grapes are left? How do we model the situation?
10. Lesson 4.7: Would not teach as prescribed. Would focus on use of the Open Array/Area Model or Partial Products. Would place amounts in contexts. Would use review problems. Would use Find and Fix My Error strategy. Visualize and sketch problem on page 273: Gina bought 2.5 pounds of peaches that cost $1.38 per pound at the grocery store. Amy went to the local farmer’s market and purchased 3.5 pounds of peaches at $0.98 per pound. Who spent more money, and how much more?
11. Lesson 4.8: Please teach conceptually. This lesson as presented is not in the spirit or intension of the CCSS! Why do we move the decimal point? So think about 4 x 0.75, in context that might mean 4 groups of 75 cents. If I use the standard algorithm, I would technically multiply the 0.75 times 100 to get 75 and then multiply that by 4 to get 300, but remember that I multiplied by 100, so to get the actual product I have divide my answer by 100…I would get 300/100 = 3 or 3.00. Another way around this is to address the units, so 4 x 0.75 is 4 groups of 75 hundredths…and I would end up with 300 hundredths or 3 wholes.
- Model this and make it real! page 277: Students are racing typical garden snails and measuring the distance the snails travel in 1 minute. Chris’s snail travels a distance of 0.2 foot. Jamie’s snail travels 0.4 times as far as Chris’s snail. How far does Jamie’s snail travel?
Activity: Try My Way with In Many Ways/DubMe App