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* *Reflection: Staircase of Complexity
Multiplication Array Part II Filling It In - Section 3: Evidence of Learning

To extend your students learning have them fill out the following chart Array, Factor, prime, composite and follow the instructions on the page.

Here is an example of student work - Exploring The Wonderful World Of Numbers Student Work

*Staircase of Complexity: Extension*

# Multiplication Array Part II Filling It In

Lesson 2 of 7

## Objective: Students will be able to design a multiplication array, while also practicing their measurement skills.

## Big Idea: A multiplication array is a visual representation of the multiplication concept that is easy for most students to understand and use.

*52 minutes*

Yesterday's lesson was about measuring out 36 squares which were 6 inches by 6 inches and drawing the grid. Today I expect students to create all multiplication fact families for each number of 1-36 using centimeter graph paper - seeing the basic facts represented in another way.

In today's world, children are being taught social skills through their peers and "screen time." Because of this I use a social emotional approach, called Tribes, in my classroom to teach collaborative and positive communication skills as well as the Common Core Standards. One Tribes strategy is to involve the students right away in their learning by asking an inclusion question. The purpose of this is to invite students to reflect on and share their own experiences - to make everyone feel included.

After my students have gotten their materials (chart, pencil, marker and rulers) and settled into their groups I ask an inclusion question because I believe that each time a group gets together students need the opportunity to feel included from the very start. This is setting them up for success in group collaboration.

*"What did you learn about math yesterday?"*

*"What was something that went well yesterday?"*

*"What is one thing that can be done to make the group work better today?"*

I give my students just enough time to cover the questions reminding them of their Tribes Agreements. Near the beginning of the year I would ask each question separately keeping the students talk on task - more teacher directed. If it is later in the year and the procedure or pattern would exist for the students to self-direct their time and keep each other on task.

#### Resources

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I start this lesson by borrowing a chart from a group that has completed their drawing in yesterday's math lesson. They have numbered across the top row and down the left columns from 1 to 6. If a group is not there yet, I suggest they make a plan to get caught up and give some examples of what other groups have done. One student measuring while the other draws the lines. Possibly they need to work together better using the skills of flexibility, effort and perseverance.

As each group finishes the grid, I model how to cut out the fact families on centimeter graph paper. Starting with a 1 × 1, 1 × 2, 1 × 3, 1 × 4, 1 × 5 and 1 × 6. Then the 2 × 1, 2 × 2, etc.

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#### Evidence of Learning

*35 min*

As students are building their array model, I walk around the room checking for understanding. I find some students do not understand there are multiple fact families for some numbers. This tells me that they do not know their basic multiplication facts.

This is common in any classroom, but expected in my multi-age classroom where some of these students are in the beginning weeks of 4th grade and may have had little experience with multiplication. For 5th graders weak with basic multiplication facts, I pair them up with a partner I know has basic facts. I am able to use peer teacher leaders with these two students.

Show Me: Fact Families for Multiple Arrays

The two peer teacher leaders are able to communicate with their partners about the reasons there are more than one fact family. One pair uses the whiteboard, where we had written all number sentences for the products of 1 - 36 while checking the homework. The student who knew their multiplication facts points out the products of 9, 12 and 24. They show their partner how they can have more than one fact family for a product.

This activity is a great beginning of the year group project because students practice their collaborative skills and it also assess students' ability to measure and create a visual model of a multiplication array.

The next day's activity uses the multiplication array charts to list factors and find prime, composite and square numbers. It was created by my fabulous teammate Cathy Mooney. You can find it in my lesson Discovering the Wonderful World of Numbers Using The Multiplication Array.

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#### Student Reflection

*5 min*

I always have my students reflect on their learning. It helps students explain and elaborate on their learning. After today's lesson, students write out their answers because today's work is related to what's coming next in the Common Core Standards in Geometric measurement: Understanding concepts of volume and relating volume to multiplication and addition (5MD.C.5) and (5NF.B.5) Interpreting multiplication as scaling or resizing.

Reflect 1, 2, 3

1. What patterns do you see in the multiplication array model?

2. What did your group do to successfully complete the model?

3. How did you personally help your group successful complete the model?

Post the charts as they are completed. I tape them to my side counter that runs along my room or over the students cubbies. I have also only posted the neatest poster in the past as an example of Personal Best work.

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- LESSON 1: Multiplication Array: Part I Measuring It Out
- LESSON 2: Multiplication Array Part II Filling It In
- LESSON 3: Mulitiplication and Divsion Assessment
- LESSON 4: Multiple Ways to Multiply With Multiple Digits
- LESSON 5: Multiples in a Minute
- LESSON 6: Multiplication Timed Test 0-10
- LESSON 7: Diving In