Estimating Sums and Differences

Focus:Students will estimate sums and differences.

Introduce:

  1. Ask students if they know the difference between an estimate and an actual answer. When is an actual answer needed and when can an estimate be used? Explain that one of the primary reasons to estimate sums and differences is to check a calculation for reasonableness.
  2. Write the following problem on the board and ask students to discuss it with their table group. Remind students to think of what the word “about” means (to estimate.)

There are 171 stamps in the Canadian stamp collection and 218 stamps in the United States stamp collection. About how many stamps are there in both collections?

  1. Discuss student’s answers with the class. Students could have solved the problem one of three ways. First, students could round each number to the nearest hundred to find 200 + 200 = 400. Second, students could have rounded each number to the nearest ten to find 170 + 220 = 290. The last way to estimate is to use compatible numbers. Compatible numbers are numbers that work together easily when adding and subtracting. Students who use this strategy might have written 175 + 225 = 400.
  2. Repeat the process with the following problem.

A third grade class has 379 items in their collection. Their goal for the week is 528 items. Estimate how many more items the class needs to collect this week in order to reach their goal.

  1. Discuss the problem with the class. First round the numbers to the nearest hundred. Then, round the numbers to the nearest ten. Finally talk about compatible numbers that could be used. One example could be 525 - 375 = 150.

Investigate:

  1. Students will work with a partner to play Estimation Compare (attached).
  2. Students will work with a partner to solve the Estimating Sums and Differences Problems (attached).

Discussion:

  1. Bring the students back together for a discussion. Ask students how they solved the problems. Specifically discuss at least one addition and one subtraction word problem.
  2. Students can complete the estimation homework page.

Estimation Compare

Materials:

Digit Cards, one deck per pair

Estimation Compare Recording Sheet

Activity:

1. Place the deck of digit cards between two players.

2. Students should take turns drawing cards until each player has 6 cards.

3. Each student should make two three digit numbers using the cards they drew.

4. Students will estimate the sum of their cards.

5. Students will compare the two sums using >, <, or =.

Example:

My estimated sum / My partner’s estimated sum / Equation to compare
500 + 200 = 700 / 100 + 300 = 400 / 700 > 400 or 400 < 700

Variations:

1. Students can estimate the difference between their two numbers.

2. Students can start the game using only four cards.

3. Students can round their numbers to the nearest ten.

Estimation Compare Recording Sheet

My estimated sum / My partner’s estimated sum / Equation to compare

Estimating Sums and Differences Problems

A book about animals has 186 pages. A book about planets has 133 pages. Jamal read both books. About how many pages did Jamal read altogether? / The Marshall family drove 231 miles to their cousin’s house in Dallas. At the gas station, the trip meter read 88 miles. About how many more miles did they drive from the gas station to their cousin’s house? / Carlos bought a book that cost $6.34 and a journal that cost $3.75. About how much money did Carlos spend on his supplies?
A farmer grew 388 tomatoes. He sold 111 of them at the farmer’s market on Thursday. About how many did the farmer have left after the sale? / Mr. Carlson’s class has 429 pennies in their collection. Ms. King’s class has 377 pennies in their collection. The classes decided to combine their collections. Estimate how many pennies they have in their combined collection. / There are 528 students in Spring Elementary School. 261 of the students are girls. About how many of the students at the school are boys?
Summer Trail school is collecting cans for recycling. Third graders collected 189 cans. Fourth graders collected 242 cans and fifth graders collected 120 cans. Estimate the number of cans the 3 grades collected altogether. / Miss Archer’s class has 714 items in their collection. Miss Brown’s class has 563 items in their collection. Estimate the number of how many more items Miss Archer’s class has than Miss Brown’s. / Jenna bought a dog collar for $7.03 and a leash for $4.92 About how much more money did the dog collar cost than the leash?

Additional Practice with Estimation

Round to the nearest ten to estimate.

1. 56 + 212. 78 – 363. 81 – 354. 72 + 61

______

Round to the nearest hundred to estimate.

5. 526 – 1826. 369 + 4317. 899 + 3928. 539 – 276

______

Use the table below to answer the following questions.

Baseball Cards Collected
Garrison / 334
Taylor / 482
Blake / 298
Reid / 365

9. About how many baseball cards did Garrison and Reid collect together?

10. Estimate how many more baseball cards Taylor collected than Blake.

11. Estimate how many baseball cards all four boys collected.