Same Perimeter, Different Shapes

10 min

Narrative

The purpose of this True or False is to elicit strategies and understandings students have for adding multi-digit numbers. It prompts students to rely on their understanding of the properties of operations and place value. The strategies used here will be helpful as students find the perimeter of shapes with repeated side lengths later in the lesson.

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 strategy.
  • Repeat with each equation.

Student Task

Decide whether each statement is true or false. Be prepared to explain your reasoning.

  • 123+75+123+75=100+100+70+70+5+5+3+3123 + 75 + 123 + 75 = 100 + 100 + 70 + 70 + 5 + 5 + 3 + 3
  • 123+75+123+75=(2×123)+(2×75)123 + 75 + 123 + 75= (2 \times 123) + (2 \times 75)
  • 123+75+123+75=208+208123 + 75 + 123 + 75 = 208 + 208
  • 123+75+123+75=246+150123 + 75 + 123 + 75 = 246 + 150

Sample Response

  • False: The expression on the right side is missing 2 twenties.
  • True: On both sides there are 2 groups of 123 and 2 groups of 75.
  • False: I know that 125+75=200125 + 75=200, so 123+75123 + 75 is less than 200.
  • True: 75+75=15075 + 75 = 150 and 123+123=246123 + 123 = 246
Activity Synthesis (Teacher Notes)
  • “How can you explain your answer without finding the value of both sides?”
Standards
Addressing
  • 3.NBT.2·Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
  • 3.NBT.A.2·Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
Building Toward
  • 3.MD.8·Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
  • 3.MD.D.8·Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

15 min

20 min