Lesson 5: Symmetry in Figures (Part 2)

Symmetry in Figures (Part 2)

10 min

Narrative

This Number Talk encourages students to think about place value and to rely on the structure of multi-digit numbers and properties of operations to mentally add multiple addends. The strategies elicited here help students develop fluency in adding multi-digit numbers. They will also be helpful when students reason about the perimeter and angles in line-symmetric figures.

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 strategy.
Keep expressions and work displayed.
Repeat with each expression.

Student Task

Find the value of each expression mentally.

$43 + 57 + 50 + 7 + 3 + 40$
$243 + 57 + 43 + 257$
$1,043 + 257 + 57 + 200 + 43 + 1,000$
$1,943 + 257 + 1 + 257 + 1,000 + 943$

Sample Response

200: There are two sets of $43 + 57$ , one of them is written in expanded form. $43 + 57 = 100$ , because $40 + 50 = 90$ , $7 + 3 = 10$ , and $90 + 10 = 100$ . Two times 100 gives 200.
600: $43 + 57 = 100$ , so $243 + 257$ is $200 + 200 + 100$ , which is 500. Adding another $43 + 57$ to 500 makes 600.
2,600:
- The expression has two sets of $257 + 43$ (just written differently), plus two 1,000s. $257 + 43 = 300$ , and twice 300 is 600. Adding the 2,000 and 600 makes 2,600.
- $257 + 243 = 500$ , $57 + 43 = 100$ , and $1,000 + 1,000 = 2,000$ , so $2,000 + 500 + 100 = 2,600$ .
4,401:
- The expression is symmetrical, with 1 in the middle and $1,943 + 257$ (written in different forms) on either side. We know that $43 + 257 = 300$ , and $1,900 + 300 = 2,200$ . Twice 2,200 is 4,400. Adding the middle 1 gives 4,401.
- $943 + 257 = 1,200$ , and $1,943 + 257 = 2,200$ . Adding 1,200 and 2,200 gives 3,400. Adding $1,000 + 1$ to 3,400 makes 4,401.

Activity Synthesis (Teacher Notes)

“How did you use the first expression to help solve the expressions that follow?” ( $43 + 57 = 100$ , so anywhere we see numbers with that combination being added, we can add 100 instead.)
Consider asking:
- “Who can restate _____’s reasoning in a different way?”
- “Did anyone have the same strategy but would explain it differently?”
- “Did anyone approach the expression in a different way?”
- “Does anyone want to add on to _____’s strategy?”

Standards

Addressing

4.NBT.B·Use place value understanding and properties of operations to perform multi-digit arithmetic.
4.NBT.B·Use place value understanding and properties of operations to perform multi-digit arithmetic.

15 min

20 min

Knowledge Components

All skills for this lesson

No KCs tagged for this lesson

Symmetry in Figures (Part 2)

10 min

Narrative

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 strategy.
Keep expressions and work displayed.
Repeat with each expression.

Student Task

Find the value of each expression mentally.

$43 + 57 + 50 + 7 + 3 + 40$
$243 + 57 + 43 + 257$
$1,043 + 257 + 57 + 200 + 43 + 1,000$
$1,943 + 257 + 1 + 257 + 1,000 + 943$

Sample Response

200: There are two sets of $43 + 57$ , one of them is written in expanded form. $43 + 57 = 100$ , because $40 + 50 = 90$ , $7 + 3 = 10$ , and $90 + 10 = 100$ . Two times 100 gives 200.
600: $43 + 57 = 100$ , so $243 + 257$ is $200 + 200 + 100$ , which is 500. Adding another $43 + 57$ to 500 makes 600.
2,600:
- The expression has two sets of $257 + 43$ (just written differently), plus two 1,000s. $257 + 43 = 300$ , and twice 300 is 600. Adding the 2,000 and 600 makes 2,600.
- $257 + 243 = 500$ , $57 + 43 = 100$ , and $1,000 + 1,000 = 2,000$ , so $2,000 + 500 + 100 = 2,600$ .
4,401:
- The expression is symmetrical, with 1 in the middle and $1,943 + 257$ (written in different forms) on either side. We know that $43 + 257 = 300$ , and $1,900 + 300 = 2,200$ . Twice 2,200 is 4,400. Adding the middle 1 gives 4,401.
- $943 + 257 = 1,200$ , and $1,943 + 257 = 2,200$ . Adding 1,200 and 2,200 gives 3,400. Adding $1,000 + 1$ to 3,400 makes 4,401.

Activity Synthesis (Teacher Notes)

“How did you use the first expression to help solve the expressions that follow?” ( $43 + 57 = 100$ , so anywhere we see numbers with that combination being added, we can add 100 instead.)
Consider asking:
- “Who can restate _____’s reasoning in a different way?”
- “Did anyone have the same strategy but would explain it differently?”
- “Did anyone approach the expression in a different way?”
- “Does anyone want to add on to _____’s strategy?”

Standards

Addressing

4.NBT.B·Use place value understanding and properties of operations to perform multi-digit arithmetic.
4.NBT.B·Use place value understanding and properties of operations to perform multi-digit arithmetic.

Symmetry in Figures (Part 2)

Warm-up Number Talk: Keeping Track 10 minKCs

Narrative

Launch

Student Task

Sample Response

Activity Half-Drawn Figures 15 minKCs

Activity What’s the Whole Picture? 20 minKCs

Knowledge Components

Symmetry in Figures (Part 2)

Warm-up Number Talk: Keeping Track 10 minKCs

Narrative

Launch

Student Task

Sample Response

Activity Half-Drawn Figures 15 minKCs

Activity What’s the Whole Picture? 20 minKCs

10 min

15 min

20 min

10 min

15 min

20 min