Grade 3: "Exploring Multiplicative Patterns"

(From: Mathology)

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This Mathology lesson plan can be accessed in both English and French by logging into your Mathology.ca/Mathologie.ca account and searching for "Patterning Activity 6: Increasing and Decreasing Patterns: Exploring Multiplicative Patterns"

Content

Big Idea: Multiplicative patterns

Expectations:

C1. Patterns and Relationships: identify, describe, extend, create, and make predictions about a variety of patterns, including those found in real‐life contexts

• Patterns: C1.2 create and translate patterns that have repeating elements, movements, or operations using various representations, including shapes, numbers, and tables of values

• Patterns: C1.4 create and describe patterns to illustrate relationships among whole numbers up to 1000

Learning Goals

We want students to...

Use an input-output machine to explore multiplicative patterns
Multiply numbers to 7 × 7

Success Criteria

I can...

use a pattern rule to explain a multiplication pattern.
show multiplication patterns on a hundred chart to help us see patterns in the products.

Materials

Student Card 20: Input-Output Machine
Math Mat 4: Hundred Chart
Math Mat 14: 10 × 10 Multiplication Chart
Counters
Exit Ticket
Practice

(All Line Masters, Student Cards, Math Mats and Practice Pages can be accessed by logging into your Mathology account)

Vocabulary

Increasing pattern
Decreasing pattern
Term
Pattern rule
Multiplication pattern
Input
Output

teacher background

Students may benefit from prior experience with:

skip-counting forward and backward
identifying, describing, creating, and extending increasing and decreasing patterns
identifying patterns on a hundred chart

Pedagogy

Minds On

Introduce an input-output machine and explain how it works.

Say, “When 1 goes in, 2 comes out. When 2 goes in, 4 comes out. When 3 goes in, 6 comes out. When 4 goes in, 8 comes out.”

Have students predict what would come out when 5 goes in and explain why they think so.

Help students see that each number is multiplied by 2, or doubled.

Record the numbers in a table and identify patterns in the input and output numbers.

Explain that "× 2" would go on the screen of the input-output machine.

Action!

Give each pair Student Card 20A and a hundred chart. Have multiplication charts and counters available.

Teacher Moves

Probing Questions:

What happens when you run a number through the machine?
How did you multiply the numbers?
What are 2 pattern rules for the machine?
What patterns do you see in the circled numbers?

LOOK-FORS:

How do students multiply the numbers (e.g., using counters; skip-counting; using a number line; using repeated addition/subtraction; using mental strategies)?
Can students describe the rule for a pattern involving multiplication?
Do students see how a pattern involving multiplication is related to skip-counting and repeated addition?
Can students identify patterns in the products circled on a hundred chart?

Consolidation Of Learning

Talk about the strategies students used to multiply (e.g., using skip-counting, repeated addition, a multiplication chart, arrays, counters) and how the strategies are related.

Have volunteers share some of the patterns they noticed in the output numbers and on the hundred chart.

Discuss the multiplicative pattern where each number is multiplied by itself (1, 4, 9, 16, 25, …). Circle the numbers on a multiplication chart and identify the pattern in their positions (e.g., on centre diagonal).

Identify the multiplicative pattern shown on this number line (e.g., multiplying by 4).

To allow students to show what they have learned in this lesson, go to the Exit Ticket and/or Practice.

Highlight for Students

We can use a pattern rule to explain a multiplication pattern.
We can show multiplication patterns on a hundred chart to help us see patterns in the products.

Supports for student learning

Accommodation: Have students use a multiplication chart (Math Mat 14) and multiply by numbers to 5 only.

Extension: Have one student secretly choose a number to multiply by, then record the input and output numbers. The other student identifies the operation in the machine. Or use Student Card 20B where students write a number from 1 to 10 on the machine and run the numbers 1 to 10 through it.

Assessment

All assessments, in the moment feedback/prompts, and independent tasks can be accessed by logging into your Mathology/Mathologie account.

SEL Self-Assessments (English) and Teacher Rubric

Extension

Log in to your Mathology.ca / Mathologie.ca account to access Intervention and Extension activities, Professional Learning Videos and Assessment tools.

Technology

If you require support logging into your Mathology/Mathologie account, please contact Kerry Stack or Erica Doucet.

Use the Pearson Hundred Chart Tool to explore patterns involving multiplication. With the Paint Brush selected, colour the numbers in a multiplication sequence (e.g., multiplying by 3). Extend the pattern, then discuss the patterns students see in the coloured numbers (e.g., numbers lie on diagonals, they alternate between odd and even).

Use the Pearson Input/Output Machine Tool to explore patterns involving multiplication. Click on the machine, then choose multiplication and the number to multiply by. Drag tiles 1, 2, 3, and 4 to the conveyor belt to run them through the machine. The results appear in the table. Talk about the patterns in the input and output numbers. Predict the output number when the input number is 5, then run the tile through the machine to check.

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