Mental math—the estimating and calculating you do in your head—is an essential part of learning math. Mental math helps students build a sense of numbers and how they work. And as students gain control and command over numbers, they gain confidence and enjoyment of math (a plus for those of you with kiddos who “hate math”.) Given how crucial mental math strategies are, I’m going share some of my favorite tips to teach mental math strategies.
Teaching 5 Key Mental Math Strategies
You can use these games and activities to teach the counting on strategy, compatible number strategy, near doubles strategy, partitioning strategy, and estimating strategy.
The Strategy—Start with the larger number of the two numbers and “count on” the smaller number. For example, if you were adding 3 + 9, you would start with the larger number (9) and then get your students to count on 3: 10, 11, 12.
This is much more efficient than beginning with the smaller number and counting on the larger number.
Practice—Students can use counters, their fingers or a number line/track to count on. Get students to first circle the larger number and then count on.
Keep it fun—Play Count On Cards. This is a simple game for 2 players.
- Remove the picture cards (Jack, Queen, King, Joker) from a deck of cards. Then separate the cards into two piles, one with the cards: ace, 2, 3 and 4 and the other pile with the cards 5 – 10. Shuffle each pile, so they’re in a random order and place face down on the playing surface. Tell students that aces act as 1 in this game.
- Have one student turn over the top two cards. They add the two numbers using the counting on strategy: count on from the larger number, and count on the smaller number. For example, if the two cards turned over were 7 and 3. They would start with 7, count on 3: 8, 9, 10.
- If the player has the correct answer, they get to keep both cards. If the answer is incorrect, the other player can try to answer the question to keep both the cards.
- Then the second player turns over two cards. Play continues until one of the piles run out of cards.
- The winner is the player with the most cards at the end of the game.
The Strategy—Explain that compatible numbers are numbers that when added produce a “tidy sum,” one that usually ends in zero, or multiples of 10. For example, 7 and 3; 6 and 4; 8 and 2; and 9 and 1 are compatible because when added they total 10 (end in zero). Also, 70 and 30; 16 and 84; 38 and 62 are also compatible numbers because when added they total 100 (end in zero).
Practice—Give students number strips of 10 or 10 counters. Have them show the different compatible number sets that add up to 10.
Keep it fun—Try this activity to help students practice with compatible numbers. Write a series of numbers on a whiteboard as shown.
Have students find compatible numbers for 10 or 100. Or challenge students to a compatible number race. See how many compatible numbers they can write down in a minute.
The Strategy—Near doubles strategy is used to add two consecutive numbers. This is an extension of doubles, which is useful since many young children learn how to double numbers pretty quickly. So if children know that 6 + 6 = 12, they can use that knowledge to figure out what 6 + 7 equals. This is the same as 6 + 6 + 1 = 13.
Practice—Use a number line to demonstrate this to students. Then ask students to try with another set of numbers, 8 + 9 for example.
Keep it fun—Play a game with number triangles. Put one number on a triangle, say 9. Ask students what the next two numbers are (10, 11). Arrange all three numbers in a triangle. Ask for suggestions of different ways to add these numbers. Write the total in the center. Highlight the near doubles strategy. You can do the same with two-digit numbers as well.
The Strategy—Partitioning is breaking numbers into parts to help simplify the math. For example, take 7 + 5. If you know that 7 + 3 = 10, you use partitioning. You first add 7 and 3 to total 10, and then add on the 2. You can use partitioning with any operation (addition, subtraction, multiplication, division). We’ll focus on addition.
Practice—Explain that you can partition numbers any way that helps you solve the problem. For example, 37 + 8 could be partitioned as
30 + (7 + 8) = 30 + 15 = 45
(37 + 3) + 5 = 40 + 5 = 45
(37 + 10) – 2 = 47 – 2 = 45
Ask students if they can think of other ways to use partitioning to solve this problem.
Keep it fun—Use a 100 grid to practice partitioning. Have students work in pairs. Each student selects a number from the 100 grid. Both students must use the partitioning strategy to add the two numbers. Have them see if they partitioned the numbers in the same way. Have them explain their thinking to their partner.
The Strategy—Estimation allows us to judge the reasonableness of responses. You can estimate in many ways: rounding, finding compatible numbers, bracketing, compensating and using benchmarks when estimating. To use a benchmark, look at a quantity and apply to a different setting. For example, if you knew that in one section of a football stadium there are 500 people, you could use that number and the number of sections to estimate the total number of people attending.
Practice—Tell students you are going to ask them to estimate how many ladybugs they see. Show a picture like the one below for 30 seconds.
Give them time to think it through and then ask for their estimates. Ask your students how they worked out their estimates. They may have counted the first row and then counted columns or noticed that there were two facing ladybugs in each column and 8 columns. Remind students that estimating isn’t about getting the “right” answer, but about determining a reasonable answer.
Keep it fun—Have students estimate how many jelly beans or similar are in a jar. Remind students this isn’t about guessing, but about estimating. Ask students to explain an approach, then test it. For example, students might pick up the jar and count how many jellybeans they can see on the bottom. Then they might try count how many layers fit in the jar. Alternately, they might ask for a small cup and see how many jelly beans fit into the cup. Then they can estimate how many cups would fit into the jar.
If you want to get numbers involved, share a game table like the one below (adjust the numbers to suit your students).
You’ll also need two dice and a calculator. One student rolls the dice and must estimate the sum of the two numbers in the matching boxes. For example, if the numbers on the dice were: 1 and 6, then the student estimates the sum of 475 + 155.
The student then selects the range that the estimate falls in. The other player uses the calculator to work out the exact answer. If this answer falls within the range selected then the first player scores a point. Play to 5 points. The player that is estimating needs to do so mentally, so no paper and pencil to work out the estimates.
Mental math can be challenging for students, but it can also be a lot of fun. The more strategies students know, the better able they are to approach math with confidence and curiosity.
Want a copy of the playing board for this estimating game (plus other downloadable math games)? I’ve made them available as an easy download.
Click here to download your FREE printable math games.
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