Multiply Two-Digit Numbers and One-Digit Numbers
10 min
Narrative
The purpose of this Warm-up is to elicit students’ prior knowledge of area and the idea that a rectangle can be decomposed into smaller rectangular regions. Students look at 4 different area diagrams they used in IM Grade 3. The reasoning will be useful when students use diagrams to multiply two- and one-digit numbers in a later activity. While students may notice and wonder many things about the number of units within the area of the gridded region, focus on the connections between the diagrams with a grid and those without.
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:
- Two rectangles are gridded and have no numbers. The other two have no grid and have numbers.
- In the first two diagrams, there are 13 squares in each row and 4 squares in each column.
- A portion of the gridded rectangle is shaded.
- Some rectangles have the side lengths marked.
- The last rectangle is partitioned into two sections.
Students may wonder:
- Where are the numbers in the gridded rectangles?
- Why is the second rectangle shaded?
- Do the four diagrams represent the same rectangle?
Activity Synthesis (Teacher Notes)
- “What do you know about the 13 and 4 in the first ungridded rectangle?” (They are side lengths. They correspond to the number of squares across and the number of squares down in the first rectangle.)
- “What about the 10, 3, and 4 in the second ungridded rectangle?” (The 10 and 3 are numbers that add up to 13. The 4 is the length of the shorter side.)
- “How are the four diagrams related? Name as many connections as you see.” (They all represent the same rectangle because they have the same side lengths and the same area. The first two show the number of square units that fit in the rectangle. The last two don’t show it but we can tell by multiplying the side lengths. The shaded portion in the second gridded rectangles show the 4×10 portion in the fourth rectangle.)
- If no students mentioned the area of the rectangles in their analysis, ask: “How might we find the area of the rectangles?” (For the gridded rectangles, we can count the unit squares or multiply the number of units across and down. For the other two, we can multiply the side lengths.)
Standards
- 4.NBT.5·Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
- 4.NBT.B.5·Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
20 min
15 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Multiply Two-Digit Numbers and One-Digit Numbers
10 min
Narrative
The purpose of this Warm-up is to elicit students’ prior knowledge of area and the idea that a rectangle can be decomposed into smaller rectangular regions. Students look at 4 different area diagrams they used in IM Grade 3. The reasoning will be useful when students use diagrams to multiply two- and one-digit numbers in a later activity. While students may notice and wonder many things about the number of units within the area of the gridded region, focus on the connections between the diagrams with a grid and those without.
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:
- Two rectangles are gridded and have no numbers. The other two have no grid and have numbers.
- In the first two diagrams, there are 13 squares in each row and 4 squares in each column.
- A portion of the gridded rectangle is shaded.
- Some rectangles have the side lengths marked.
- The last rectangle is partitioned into two sections.
Students may wonder:
- Where are the numbers in the gridded rectangles?
- Why is the second rectangle shaded?
- Do the four diagrams represent the same rectangle?
Activity Synthesis (Teacher Notes)
- “What do you know about the 13 and 4 in the first ungridded rectangle?” (They are side lengths. They correspond to the number of squares across and the number of squares down in the first rectangle.)
- “What about the 10, 3, and 4 in the second ungridded rectangle?” (The 10 and 3 are numbers that add up to 13. The 4 is the length of the shorter side.)
- “How are the four diagrams related? Name as many connections as you see.” (They all represent the same rectangle because they have the same side lengths and the same area. The first two show the number of square units that fit in the rectangle. The last two don’t show it but we can tell by multiplying the side lengths. The shaded portion in the second gridded rectangles show the 4×10 portion in the fourth rectangle.)
- If no students mentioned the area of the rectangles in their analysis, ask: “How might we find the area of the rectangles?” (For the gridded rectangles, we can count the unit squares or multiply the number of units across and down. For the other two, we can multiply the side lengths.)
Standards
- 4.NBT.5·Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
- 4.NBT.B.5·Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.