Patterns in the Multiplication Table
10 min
Narrative
The purpose of this Warm-up is to revisit the idea that the product of two factors in the multiplication table is found where the row and column of each factor intersect. While students may notice and wonder many things about these products, the patterns in the multiplication table and how the table is structured are the important discussion points.
Launch
- Groups of 2
- Display the image.
- “What do you notice? What do you wonder?”
- 1 minute: quiet think time
Teacher Instructions
- “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Share and record responses.
Student Task
What do you notice? What do you wonder?
Sample Response
Students may notice:
- The numbers in the top row and the leftmost column are factors.
- The product is lined up with a factor on the top and a factor to the left.
- The row that starts with 5 counts by 5 as you move to the right: 5, 10, 15, 20, 25.
- The column that starts with 2 counts by 2 as you move down the column: 2, 4, 6, 8, 10.
- There are many patterns in the table.
- The table is like some tables we saw before, but those tables had to do with addition.
- What do the numbers in the table mean?
- How does the table work?
- Why are the numbers smaller in the top left part of the table, then larger in the bottom right part of the table?
Activity Synthesis (Teacher Notes)
- If not mentioned in students’ responses, explain: “A multiplication table uses rows and columns to show products of two numbers. The numbers in the leftmost column and the top row are factors.”
- “Each number in the (non-shaded part of the) table is the result of multiplying the two factors in the same row and column as that number.”
- Ask questions to invite students to explain some of the patterns they noticed in the table. For each question, give students a minute of quiet think time. Record their responses with equations, if possible.
- If students do not notice the following patterns, consider asking:
- “Did you notice any places where the same number was in the non-shaded part of the table? Where do you see this? Why does this happen?” (The number 15 appears in two places because we can find 3×5 or 5×3 to get 15. The order of the factors doesn’t change the result. We see 12 in two places in the table because we can get 12 by counting by 3 like 3, 6, 9 12 or counting by 4 like 4, 8, 12.)
Standards
Addressing
- 3.OA.9·Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. <em>For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.</em>
- 3.OA.D.9·Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. <span>For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.</span>
20 min
15 min
Knowledge Components
All skills for this lesson
Role Legend
Target
Essential
Supporting
Foundational
All lesson KCs
2 skills
Press enter or space to select a node. You can then use the arrow keys to move the node around. Press delete to remove it and escape to cancel.
Press enter or space to select an edge. You can then press delete to remove it or escape to cancel.
Patterns in the Multiplication Table
10 min
Narrative
The purpose of this Warm-up is to revisit the idea that the product of two factors in the multiplication table is found where the row and column of each factor intersect. While students may notice and wonder many things about these products, the patterns in the multiplication table and how the table is structured are the important discussion points.
Launch
- Groups of 2
- Display the image.
- “What do you notice? What do you wonder?”
- 1 minute: quiet think time
Teacher Instructions
- “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Share and record responses.
Student Task
What do you notice? What do you wonder?
Sample Response
Students may notice:
- The numbers in the top row and the leftmost column are factors.
- The product is lined up with a factor on the top and a factor to the left.
- The row that starts with 5 counts by 5 as you move to the right: 5, 10, 15, 20, 25.
- The column that starts with 2 counts by 2 as you move down the column: 2, 4, 6, 8, 10.
- There are many patterns in the table.
- The table is like some tables we saw before, but those tables had to do with addition.
- What do the numbers in the table mean?
- How does the table work?
- Why are the numbers smaller in the top left part of the table, then larger in the bottom right part of the table?
Activity Synthesis (Teacher Notes)
- If not mentioned in students’ responses, explain: “A multiplication table uses rows and columns to show products of two numbers. The numbers in the leftmost column and the top row are factors.”
- “Each number in the (non-shaded part of the) table is the result of multiplying the two factors in the same row and column as that number.”
- Ask questions to invite students to explain some of the patterns they noticed in the table. For each question, give students a minute of quiet think time. Record their responses with equations, if possible.
- If students do not notice the following patterns, consider asking:
- “Did you notice any places where the same number was in the non-shaded part of the table? Where do you see this? Why does this happen?” (The number 15 appears in two places because we can find 3×5 or 5×3 to get 15. The order of the factors doesn’t change the result. We see 12 in two places in the table because we can get 12 by counting by 3 like 3, 6, 9 12 or counting by 4 like 4, 8, 12.)
Standards
Addressing
- 3.OA.9·Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. <em>For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.</em>
- 3.OA.D.9·Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. <span>For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.</span>