##
* *Reflection: Data Analysis
Multiplying with Decimals - Section 6: Closure and Ticket to Go

Looking at students’ work on this ticket to go showed me the different stages my students were at in multiplying decimals. I grouped students in the following categories:

**Novice: **These students struggled with basic multiplication facts and working with decimals. Some of these students are only comfortable using the box method for multiplication. This method works best with smaller whole numbers. This student in particular was able to multiply the numbers but didn’t understand where the decimal point needed to go. It seems like this student made her estimate after she did the work and picked a round number that was near her answer, rather than using her number sense to make an estimate first. These students need extra instructional time to learn the traditional method of multiplication and how to use it with decimals. Unit 2.3 Student Work N.jpeg

**Approaching Mastery:** These were able to multiply using decimals, but only inconsistently. Most of these students were able to correctly find the product of problem one. The problem came with where to put the decimal point in problem 2. Most of these students incorrectly answered 0.35 instead of 0.035. Most of these students were able to make reasonable estimates. Unit 2.3 Student Work AM.jpeg

**Proficient:** These students were able to use the traditional algorithm to multiply decimals and they were able to make reasonable estimates.Unit 2.3 Student Work P.jpg

For this situation, I did not include an “advanced” category because the content did not require students to explain or analyze their work. Most of my students fell in the Approaching Mastery and Proficient categories. I will review the common mistakes in the next lesson, Multiplying with Decimals Day 2. For the novice students I will find time to work on the traditional algorithm with them.

*Data Analysis: Ticket to Go Reflection*

# Multiplying with Decimals

Lesson 4 of 16

## Objective: SWBAT: • Make estimates of multiplication problems involving decimals • Multiply multi-digit decimals together

#### Do Now

*5 min*

See my **Do Now** in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day. Here, I want students to connect their knowledge of fractions to decimals. I also want them to apply what they did in the previous lesson **(Adding and Subtracting Decimals)** to answer number 3.

I ask students if they have an efficient way of counting the shaded boxes. For number three I ask for a volunteer to explain how we can use estimation to answer this question. I want students to recognize that if you are starting with the same amount (1) then 1 – 0.001 has a larger answer because you are subtracting a smaller piece. If students struggle with this, I ask them first to compare 0.01 and 0.001. 0.01 is one hundredth or 1/100. 0.001 is one thousandth or 1/1000. Which decimal is smaller? How do you know? Then I give an example using whole numbers. Which answer is larger 10 – 2 or 10 – 3?

I also have a volunteer show and explain his/her work showing the procedure of subtracting the decimals. Some students will struggle with regrouping. Other students will struggle with figuring out how to line up the numbers. I have even seen some students stack up 0.01 – 1 (with the 1 under the hundredths place) because they do not realize which number is larger. I look for these mistakes and review them with the class.

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#### Estimation

*5 min*

Here I want students to quickly review the vocabulary word product and then work on estimating. I give students a couple minutes to make and write explanations for their estimates. I stress to students that estimates need to be relatively quick.

I walk around and monitor student work. I’m looking to see what strategies students are using. Some students may round numbers to whole numbers and multiply. Other students may make connections to fractions or percent. For example, for number 2 a student may recognize that 0.5 is equal to ½ and find ½ of 10.

I call one student to explain one of their estimates. These students are students I observed using a particular strategy as I was walking around. I am not giving exact answers at this time. We will work on finding exact products later in the lesson. It is important that students are able to use their number sense to make reasonable estimates.

#### Resources

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#### Problems

*10 min*

I have a student read problem 1. I ask students to make an estimate. Do you think it is more or less than 12 liters? Why? Then I ask them to work on the two problems independently. I stress that there are many ways they can find their answer, it is important that they show their work. Some students may struggle and this is okay. I want them to do most of the heavy lifting during this lesson so that they understand what is happening when we multiply with decimals. Students are engaging with **MP1: Make sense of problems and persevere in solving them**.

As students work, I walk around and monitor their progress. I am taking note of different strategies students are using. If a student finishes problems before other students, I prompt them to find other ways of finding the same answer. If students are struggling with working with decimals I will give them 10x10 grids to represent the decimals.

For problem one, some students may add 3.7 four times. Other students may double 3.7 and then double their answer. Other students may multiply 3 x 4 and then add up 0.7 four times. Other students may make connections with their knowledge of adding or multiplying fractions. Other students may be familiar with the algorithm.

I ask 3 students to share and explain their work for #1. If I don’t see one of the strategies I have mentioned, I will present it and ask students if it works and why or why not. Then I ask students to compare our answer with our estimate. How did we do? Does our answer make sense?

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A common struggle with students is that they do not know where the decimal point should go in their product. The first step is that they can estimate to see if their answer makes sense. I **Create Homogeneous Groups **using data from the ticket to go from **Adding and Subtracting Decimals. **

I have a volunteer read the task and pass out the calculators. I give students 3-5 minutes to make their estimates and calculate their answers. I walk around to ensure that students are on tasks and write neatly.

We come back together as a class. I ask students to think about what patterns they notice in their answers and what questions they have. I read the directions for “Comparing Sets” and explain that they will participate in a **Think Write Pair Share. **Students are engaging in **MP8: Look for and express regularity in repeated reasoning **and **MP3:**** ****Construct viable arguments and critique the reasoning of others.**

Then I ask for volunteers to share out with the class. What patterns did you and your partner notice? I want students to see the relationship between the number of decimal places in the factors and the number of decimal places in the product. We test their ideas using the problems in Set A and Set B.

I have a volunteer collect the calculators.

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#### Practice

*15 min*

We do number 1 and 2 together. I ask students how they want to find the exact product. I also show them the algorithm. I stress that students need to use their number sense and the patterns they noticed earlier to decide if their final answer makes sense.

Students work independently on the rest of the problems. They can check in with their partner if they are stuck. I **Post A Key **so that students can check their work when they finish a page. I am looking that students are making reasonable estimates and that they are successfully multiplying the decimals using a strategy of their choice.

If students successfully complete the practice problems, they can work on the college practice problems.

If students are struggling, I may intervene in one of the following ways:

- Ask them what their estimate is and how they got it.
- Give them a word problem situation that represents the problem.
- Pull a small group of students who are struggling to work together.

#### Resources

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#### Closure and Ticket to Go

*10 min*

I begin the **Closure **by asking students to look at questions 2 and 3. What do you notice? How did you find the exact product. I want students to notice that the answers were the same. Why is it? I want students to recognize that 0.6 is equal to 0.60 and that .24 (or 24/100) is equivalent to .240 (240/1000). Then I ask students to share out how they found their estimates for number 6. How did you find the exact product? I have a student show and explain his/her work.

With about five minutes left I pass out the **Ticket to Go **for students to complete independently. Then I pass out the **HW Multiplying with Decimals.**

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- UNIT 1: Intro to 6th Grade Math & Number Characteristics
- UNIT 2: The College Project - Working with Decimals
- UNIT 3: Integers and Rational Numbers
- UNIT 4: Fraction Operations
- UNIT 5: Proportional Reasoning: Ratios and Rates
- UNIT 6: Expressions, Equations, & Inequalities
- UNIT 7: Geometry
- UNIT 8: Geometry
- UNIT 9: Statistics
- UNIT 10: Review Unit

- LESSON 1: Pretest
- LESSON 2: Going to College
- LESSON 3: Adding and Subtracting Decimals
- LESSON 4: Multiplying with Decimals
- LESSON 5: Multiplying with Decimals Day 2
- LESSON 6: Dividing with Decimals
- LESSON 7: Dividing with Decimals Day 2
- LESSON 8: Dividing with Decimals Day 3
- LESSON 9: Mixed Operation Practice + Scholarships
- LESSON 10: Show what you know + Equivalency
- LESSON 11: Loans and Savings
- LESSON 12: Budgets
- LESSON 13: College Project Wrap Up
- LESSON 14: Unit Review Stations
- LESSON 15: Unit Closure
- LESSON 16: Unit Test