Moose Math Day 3

Write the following numbers in EXPANDED FORM!

523

570,408

879,002

Ten Minute Math

Answers!

523= 500 + 20 + 3

570,408= 500,000 + 70,000 + 400 + 8

879,002=800,000 + 70,000 + 9,000 + 2

Ten Minute Math

Examining the U.S. AlgorithmToday we’re going examine a subtraction strategy and notation that a number of people use-the US algorithm for subtraction.

When people use the US algorithm, they start from the ones place. To help us understand this strategy better, first let’s write each number in EXPANDED FORM.

The expanded form is written in parentheses to show that we are subtracting ALL the parts. We start with the ones place, but we do not want to subtract 7 from 3. We want to change the way we’re breaking apart this number so that we get only POSITIVE differences. We’re going to break up the 80 and combine part of it with the 3.

283- 137

283 (200 + 80 + 3)- 137 - (100 + 30 + 7)

Examining the U.S. AlgorithmThe expanded form is written in parentheses to show that we are subtracting ALL the parts. We start with the ones place, but we do not want to subtract 7 from 3. We want to change the way we’re breaking apart this number so that we get only POSITIVE differences. We’re going to break up the 80 and combine part of it with the 3.

Talk to your shoulder partner about what number you think should go in the blank.

What is 13 - 7?

This is what is called “borrowing” or regrouping. We didn’t have enough ones to subtract from to get a positive number, so we used one of the 8 tens and added it to the 3.

Then instead of 200 + 80 + 3, we had 200 + 70 + 13, which is the same amount just broken up differently.

283 (200 + 80 + 3) (200 + 70 + ___)- 137 - (100 + 30 + 7)

283 (200 + 80 + 3) (200 + 70 + 13)- 137 - (100 + 30 + 7) - (100 + 30 + 7)

6

Examining the U.S. Algorithm

The Standard algorithm is a “short hand” notation instead of writing out the new way to break the number apart like we did. Let’s look at the notation.

Listen as I walk you through the algorithm.

I do not want to subtract 7 from 3, so I take a ten from the tens place and give it to the ones place. I show this by crossing out the 8, making it a 7, and writing a 1 next to the 3 to make it 13 ones.

13 minus 7 is 6.

Then, 7 minus 3 is 4 (that’s 7 tens minus 3 tens)

Then 2 minus 1 is 1. What do the 2 and 1 mean?

(200 + 70 + 13)- (100 + 30 + 7)

640100

(200 + 70 + 13)- (100 + 30 + 7)

640100

283- 137

283- 137

7 13

641

Complete by subtracting the tens and hundreds.

Look at the tens place.

Do we need to borrow from the hundreds place?Are we ready to subtract?

Examining the U.S. AlgorithmLet’s work another example. Solve this example in expanded form and by using the algorithm.

Look at the ones place.

Do we need to borrow from the tens place?

545- 268

(500 + 40 + 5)- (200 + 60 + 8)

(500 + 30 + 15)- (200 + 60 + 8)

(400 + 130 + 15)- (200 + 60 + 8)

770200

Let’s try this same problem with the Algorithm.

I do not want to subtract 8 from 5, so I take a ten from the tens place and give it to the ones place. I show this by crossing out the 4, making it a 3, and writing a 1 next to the 5 to make it 15 ones.

15 minus 8 is 7.

I do not want to subtract 6 from 3, so I take a hundred from the hundreds place and give it to the tens place. I show this by crossing out the 5, making it a 4, and writing a 1 next to the 3 to make it 13 TENS.

Then, 13 minus 6 is 7 (that’s 13 tens minus 6 tens)

Then 4 minus 2 is 2.

Examining the U.S. Algorithm (500 + 40 + 5)- (200 + 60 + 8)

(500 + 30 + 15)- (200 + 60 + 8)

(400 + 130 + 15)- (200 + 60 + 8)

770200

545- 268

3 15

772

41

Examining the U.S. AlgorithmIndependent Work: Solve the following problems using the algorithm

1.757 - 428

2. 526 - 188

3. 361 - 143

4. 844 - 757

5. 498 - 279

6. 525 - 164