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Addition: Partial Sum, Blocks Addition, and Estimation

Grade 3
Jul 30, 2023


The total bill for a certain thing is 246.

The customer paid in the given denominations.

From this, we can say how he used hundreds, tens, and ones.

hundred’s, ten’s and one’s
hundred’s, ten’s and one’s
The customer paying
The customer paying

Ones, tens, and hundreds place:

  • A number can have many digits and each digit has a special place and value. Starting from the right the first digit will be at one place, the second digit at the tens place, and the third digit at the hundred’s place.

Example:   H T O

                 1 0 0


Place Value:

In math, every digit in a number has a place value. Place value can be defined as the value represented by a digit in a number on the basis of position.

Example: In number 850, 5 represents 5 tens or 50, however the 1 in 1000 represents 1 thousand or 1000.


Base ten blocks are used to represent numbers as a base ten model. Base ten blocks mimic the base ten number system by representing the ones, tens, hundreds, and thousands of places.


Estimation Sum

  • The whole numbers are first rounded as specified, i.e., rounded to the nearest ten, hundred, and so on. Then the sum of the rounded whole numbers is found to estimate the sum of the whole numbers.
  • When rounding, follow these rounding rules: If the number being rounded is less than 5, round down or else round up.


Estimation Sum
Estimation Sum

Sol:  26 has to round up near ten, i.e., 30.


         And 12 has to round down near ten, i.e., 10.

         Total sum is 40.

Word Problems on Adding Numbers by Using Blocks

Example 1:

Margot counted 244 manatees one year and 178 manatees the next. How many manatees did Margot count all together?

Adding numbers by using blocks
Adding numbers by using blocks


First estimate and then use the place value to add the numbers.

244 is about 200

178 is about 200

200 + 200 = 400

The sum is about 400 manatees.

Add each place value. Start with hundreds.


+ 178

     300   2 hundreds + 1 hundred

     110   4 tens + 7 tens

    +  12   4 ones + 8 ones


300, 110 and 12 are partial sums.

300, 110 and 12 are partial sums

244 + 178 = 422 manatees.

Example 2:

A school cafeteria sold 225 lunches on Monday, 140 lunches on Tuesday, and 226 lunches on Wednesday. Did the cafeteria sell more lunches on Monday and Tuesday or Tuesday and Wednesday? Use place-value blocks or drawing to solve.


Lunch boxes sold on Monday = 255

Example 2
Example 2

Lunch boxes sold on Tuesday = 140

Lunch boxes sold on Wednesday = 226
Lunch boxes sold on Wednesday = 226
Lunch boxes sold on Monday and Tuesday
Lunch boxes sold on Monday and Tuesday
Number of lunch boxes sold on Tuesday and Wednesday
Number of lunch boxes sold on Tuesday and Wednesday

Number of lunch boxes sold on Monday and Tuesday = 255 + 140 = 395

Number of lunch boxes sold on Tuesday and Wednesday = 140 + 226 = 366

The drawing of blocks tables
The drawing of blocks tables

By observing the drawing of blocks tables. The lunchboxes sold on Monday and Tuesday are more than Tuesday and Wednesday.  


(1 – 5) Estimate the sum

  1. 324 + 135                   
  2. 163 + 225                   
  3. 456 + 322                   
  4. 158 + 256                   
  5. 752 + 354
  6. Henry believes the sum of 275 + 313 is 598. Is that correct? Use place-value blocks or partial sums in the explanation.
Partial Sum
Partial Sum

7. There are 18 boys and 19 girls in Mrs. Olive’s class. How many kids are there in Mrs. Olive’s class?

Concept Summary:

Concept Summary
Concept Summary

What We Have Learned:

  • Partial sums using place values.
  • Blocks addition.
  • Estimation.
Partial Sum


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