Topic 9 L 1-4

Adding with Partial Sums

100

580 + 315 = 

580  ---- 500 + 80 + 0

315 ----- 300 + 10 + 5

______________________

 895        800 + 90 + 5

200

Break 627 + 361 apart by place value. Find the sum.

600 + 20 + 7

300 + 60 + 1

___________

900 + 80 + 8 = 988

300

Paul needs to find 318 + 230. What three smaller problems can he break this addition problem into? What is the sum?

         318 

+       200

__________

           518

+           10

___________

            528

      

        528 

+         0

_________

         528

400

Using the expanded form below, write the standard form of both numbers in an equation and solve.

400 + 10 + 5 ; 800 + 50 + 3

415 + 853 = 

400 + 800 = 1,200

10 + 50 = 60 

5 + 3 = 8

1,200 + 60 + 8 = 1,268

500

Is Sarah's work correct? If not, tell why and write a correct answer.

Find 64 - 27

I can add 3 to 27 to get 30.

64 - 30 = 34

34 - 3 = 31

So, 64 - 27 = 31

Yes, she is correct. 

Adding 3 to 27 helps to make mental math happen.

3 + 27 = 30

64 - 30 = 34

34 - 3 = 31

She needs to subtract the 3 that she added to 27 in the beginning. 

Regrouping to Add

100

118 + 146 = ?

264

200

54 + 46 = ?

100

300

118 + 146 = ?

264

400

283 + 147 + = ?

427

500

Will there be any regrouping in the following problem? How do you know?

89 + 41 = ?

Yes

I know because when you add 9 ones and 1 one it equals 10 ones. Ten ones needs to be regrouped as one group of 10 and carried over to the tens place. 

Adding 3 or More Numbers

100

35 + 63 + 76 = ?

174

200

149 + 22 + 314 = ?

485

300

293 + 312 + 78 = ?

683

400

46 + 461 + 309 = ?

816

500

56 + 102 + 314 + 493 = ?

965

Subtracting with Partial Differences

100

56 - 14 = ?

     56 

-    10

______

    46

-     4

_______

     42

200

248 - 156 = ?

      248 

-     100

________

      148

-      50

________

        98

300

365 - 138 = ?

        365 

-       100 

__________

         265

-          30

___________

         235

-           8

__________

          227

400

756 - 642 = ?

      756 

-     600

________

      156

-       40

_________

        116

-           2

__________

         114

500

Josh need to find 455 - 364. His work is below. Explain what is incorrect and find the correct answer. 

455 - 300 = 155

155 - 50 = 105

105 - 4 = 101

His work is incorrect because he subtracted a partial difference of 50 instead of 60, which is in the original number. His second subtraction should be 155 - 60 = 95. Then 95 - 4 = 91.

The difference is 91. 

Review

100

What number is in the 100s place? What is it worth?

4,578

200

Round 567 to the nearest 100 and the nearest 10. 

567 rounds to 600

567 rounds to 570

300

Write the following number in expanded form.

3,602

3,000 + 600 + 2

OR

3,000 + 600 + 0 + 2

400

36 / 4 = ?

9

9 x 4 = 36

500

67 x 8 = ?

536