The purpose of this Warm-up is to draw students’ attention to the first few multiples of 45, which will be helpful as students continue to work with benchmark angles and use a protractor to measure angles. Students have the skills to perform the multiplication in each equation, but computing each product may be time-consuming. Students can more efficiently tell if the equations are true or false if they consider properties of operations and look for and make use of structure.
Launch
Display one equation.
“Give me a signal when you know whether the equation is true and can explain how you know.”
1 minute: quiet think time
Teacher Instructions
Share and record answers and strategies.
Repeat with each statement.
Student Task
Decide if each statement is true or false. Explain your reasoning.
2×45=6×15
4×45=2×90
3×45=180−90
6×45=45+90+135
Sample Response
True: the 45 on the left side is 3×15, and the 6 on the right is 2×3. Both sides are 2×3×15.
True: 2×90 is 2×2×45, which is equal to 4×45.
False: the right side is 90, which is 2×45, so the 3×45 on the left side cannot also be 90.
True: the right side is (1×45)+(2×45)+(3×45), which is equal to 6×45.
Activity Synthesis (Teacher Notes)
Some students may notice that it is handy to think in terms of 2×45 because it would mean dealing with multiples of 90 rather than with multiples of 45. Highlight their explanations.
If no students decomposed expressions such as 3×45, 4×45, and 6×45 into sums of 1×45 and 2×45, discuss how this could be done. (See Sample Responses.)
Standards
Addressing
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.
15 min
20 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Use a Protractor to Measure Angles
10 min
Narrative
The purpose of this Warm-up is to draw students’ attention to the first few multiples of 45, which will be helpful as students continue to work with benchmark angles and use a protractor to measure angles. Students have the skills to perform the multiplication in each equation, but computing each product may be time-consuming. Students can more efficiently tell if the equations are true or false if they consider properties of operations and look for and make use of structure.
Launch
Display one equation.
“Give me a signal when you know whether the equation is true and can explain how you know.”
1 minute: quiet think time
Teacher Instructions
Share and record answers and strategies.
Repeat with each statement.
Student Task
Decide if each statement is true or false. Explain your reasoning.
2×45=6×15
4×45=2×90
3×45=180−90
6×45=45+90+135
Sample Response
True: the 45 on the left side is 3×15, and the 6 on the right is 2×3. Both sides are 2×3×15.
True: 2×90 is 2×2×45, which is equal to 4×45.
False: the right side is 90, which is 2×45, so the 3×45 on the left side cannot also be 90.
True: the right side is (1×45)+(2×45)+(3×45), which is equal to 6×45.
Activity Synthesis (Teacher Notes)
Some students may notice that it is handy to think in terms of 2×45 because it would mean dealing with multiples of 90 rather than with multiples of 45. Highlight their explanations.
If no students decomposed expressions such as 3×45, 4×45, and 6×45 into sums of 1×45 and 2×45, discuss how this could be done. (See Sample Responses.)
Standards
Addressing
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.