Area and Addition

10 min

Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for adding two numbers when one number is close to a multiple of 10. These understandings help students develop fluency and will be helpful later in this lesson when students add the areas of parts of a figure to determine the area of the whole figure.

When students use the fact that one number is close to 10 to find the sum, they look for and make use of structure (MP7).

Launch

  • Display one expression.
  • “Give me a signal when you have an answer and can explain how you got it.”
  • 1 minute: quiet think time
Teacher Instructions
  • Record answers and strategies.
  • Keep expressions and work displayed.
  • Repeat with each expression.

Student Task

Find the value of each expression mentally.

  • 9+69 + 6
  • 29+629 + 6
  • 59+659 + 6
  • 49+849 + 8
Solution Steps (4)
  1. 1
    Add 9 + 6 by making 10
    →9 + 1 = 10, then 10 + 5 = 15
  2. 2
    Add 29 + 6 by making 30
    →29 + 1 = 30, then 30 + 5 = 35
  3. 3
    Add 59 + 6 by making 60
    →59 + 1 = 60, then 60 + 5 = 65
  4. 4
    Add 49 + 8 by making 50
    →49 + 1 = 50, then 50 + 7 = 57

Sample Response

  • 15: I just know it. I took away 1 from 6 and added it to the 9 to make 10, and then added the leftover 5, which makes 15.
  • 35: I took away 1 from 6 and added it to the 29 to make 30, and then added the leftover 5 to make 35.
  • 65: I changed 59 to 60, and then added 6 to get 66. Then I subtracted 1 to make up for the extra 1, which makes 65.
  • 57: I took away 1 from the 8 and added it to the 49 to make 50, and then added 50 and 7 to get 57.
Activity Synthesis (Teacher Notes)
  • “What pattern do you see as you look at the expressions and their values? Why is that happening?” (Each of the first addends has a 9 in the ones place. You can make a ten for each expression. The number in the ones place of the value of each expression is 1 less than the second addend. This is because you can take 1 from each addend to make a ten with the first addend.)
  • As needed, record students’ thinking, using a number line or base-ten diagram.
  • Consider asking:
    • “Did anyone notice a different pattern”?
    • “Did anyone notice the same pattern but would explain it differently?”
Standards
Building On
  • 2.NBT.5·Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
  • 2.NBT.B.5·Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
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>
Building Toward
  • 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.

15 min

20 min