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### Math Topics

Place ValueThe students have been learning place value and that each number has a value depending on where it is located in a number. We used the place value chart to show the differences in the ones, tens, hundreds, and thousands places. The students discovered that the number: 4, 568 has different values. Such as the 8 in the ones place is 8, the 6 in the tens place has a value of 60, the 5 in the hundreds place has a value of 500, and the 4 in the thousands place has a value of 4,000. We used place value blocks to show how different numbers can be made and changed.

Forms of Writing Numbers

Standard Form: This is a fancy way of saying a regular number. (4, 568)

Expanded Form: The number is stretched out to show the different place values. (4,000+500+60+8=4,568)

Word Form: The number is written down in words. (Four Thousand Five Hundred Sixty Eight)

Compare Numbers Up to 10,000 Place

Greater Than: >

Less Than: <

Equal To: =

Remind your child that the "alligator" always chomps down on the larger amount.

Order Numbers Up to 10,000 Place

Students will need to order numbers from least to greatest or from greatest to least.

For example: 1, 246; 5, 824; 1, 252

Greatest to Least: 5, 824; 1, 252; 1, 246

Least to Greatest: 1, 246; 1, 252; 5, 824

Another way they may ask a question like this is:

What is the smallest possible number you can make from these digits?

5 4 3 8

3, 458

What is largest possible number you can make from these digits?

5 4 3 8

8, 543

If you are comparing the two numbers 10, 546 and 10, 559, the students will look at the biggest place value first and compare. If the number is the same, then we say the alligator can't make a decision and they need to move to the next place value and so on, until the alligator can choose the biggest number. 10, 546 < 10, 559 Read this number as 10, 546 is less than 10, 559.

Rounding to the Nearest 10

549

Step 1: Underline the 10's place. This will help you decide which two tens 49 falls between.

Step 2: Draw an arrow underneath the four. Write 40 below the arrow. This tells you it could round down to 40.

Step 3: Draw an arrow above the four. Write 50 above the arrow. This tells you it could round down to 50.

Step 4: Circle the 9. This tells you whether you are going to round up or down.

0, 1, 2, 3, 4 Hit the floor. (Round Down)

5, 6, 7, 8, 9 Raise the vine. (Round Up)

Step 5: The 9 is in the round up category so the number would round up to 550.

Round to the Nearest 100 Place

You will follow the same steps as above, but underline the 100s place to tell you which two 100s it could round to, and circle the tens place to tell you to round up or down.

Estimating Sums

(Rounding) (Add)

When you estimate a sum, you will round the numbers either to the nearest 10s or 100s place. You will then add the two rounded numbers together to get an answer that is an estimate of the sum. Tests will ask this question in many different ways such as "Fred has 245 stickers and Bob has 546, about how many stickers do they have altogether?" '' Estimate the sum of 126+245 to the nearest 100."

Estimating Differences

(Rounding) (Subtract)

When you estimate a difference, you will round the numbers either to the nearest 10s or 100s place. Then subtract the two rounded numbers to get an answer that is an estimate of the difference.

Adding Two-Digit Numbers

Rule 1: Line up the numbers by place value.

Rule 2: ALWAYS start in the ones place.

Rule 3: Work from top to bottom.

Example 1: 25+32= Have your child line up the place values and then add 5+2 and then 2+3.

Example 2: 37+45= When you have to re-group ("carry" to us who went to school more than 10 years ago), I still have my kids start in the ones place and add up 7+5=, but when they get that answer I have them arrow over to the right and write down the answer to the ones place to make it easier for them to put the ones with the ones and the tens with the tens. Then add the tens place, starting from the top with the re-grouped one and working our way down to 3 and then 4.

Adding Three Digit Numbers

** The rules remain the same.**

Example 1: 342+232= Add 2+2, then 4+3, then 3+2.

Example 2: 546+245= Add 6+5, arrow over to the right and write down the 11, put the one in the ones place and the other one above the tens place, add the 1+4+4, then add the hundreds 5+2.

Example 3: 268+379= When you need to re-group twice, have them arrow over to the right for the ones place and over to the left for the tens place. Add 8+9, arrow the 17 to the right of the ones, put the 7 under the ones place and re-group the 1 over the tens place, add from top to bottom in the tens place 1+6+7=14, arrow the 14 to the right of the plus sign, place the four under the tens and the one on top of the hundreds, finally add the hundreds from top to bottom 1+2+3=6.

Subtracting Two and Three Digit Numbers without Regrouping

1. Line up the place values.

2. Start in the ones place.

3. Ask yourself can I subtract these two numbers. If yes, then subtract through the place values. If no, please see subtracting with regrouping.

4. Check your work by adding the answer to the second number. If you get the third number, you are right!!! If you do not get the third number, then go back and check your work.

Example 1: 49 17

-32 +32

_____ ______

17 47

Example 2: 145 13

-132 +132

_____ _____

013 145

Subtracting Two and Three Digit Numbers With Regrouping (Borrow and Carrying for the old school people like me!)

1. Line up the place values.

2. Start in the ones place.

3. Ask yourself can I subtract the bottom number from the top number. If no, then you need to go next door to the tens and borrow one ten. Cross out the number in the tens place and make it one less, add the ten that you borrowed to the number in the ones place and subtract.

5. Check your work with addition.

Fact Families and Missing Numbers

With addition and subtraction fact families there are always 2 addition number sentences and 2 subtraction number sentences.

For example:

3, 5, 8

3+5=8

5+3=8

8-3=5

8-5=3

When looking at fact family problems students may also have to find a missing number.

For Example:

560- * = 235

so, they would need to subtract 560-235= 325.

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