We use mental math every day, and some of it is so ingrained we may not even think about it. And while students may ask, “Can’t we just use a calculator or computer?” when it comes to doing math in their heads, there are a lot of reasons to teach mental math.
Students who can do mental math increase their number sense and do math with more fluency and ease. Frequent mental math helps students build confidence as well. Given the high levels of math anxiety seen in students (and often their parents as well), we certainly want to increase math confidence.
How to teach mental math
When we talk about mental math, we’re not talking just about adding things up in your head. We’re talking about specific skills or strategies that help students do a variety of math functions in their heads. Five core mental math strategies students should know are:
- Counting on
- Near doubles
- Compatible numbers
- Estimating strategy
Here’s what you need to know about each of them.
Students often understand how to count on, but need to learn to do it efficiently. For example, say you tell students that Jamila had 4 apples and Joe gave her 7 more and ask how many Jamila now has. Some students may have learned that 4 + 7 = 11, but those who haven’t will count on, perhaps using fingers or counters.
Students need to learn to count on from the higher number. So in this case, start with 7 and count on 4. Show them that you get the same answer either way and explain that it is quicker to add on the smaller number.
Once students have learned how to double numbers, it’s time for the near doubles strategy. Explain that we use the near doubles strategy to add two consecutive numbers.
Use counters to show this concept. Have students count out two groups of 3 counters. Then have them add a group of 1. Have them count all the counters. Then have them move the 1 group into one of the groups of 3 (making groups of 3 and 4). Have them count the counters again.
This strategy helps them add numbers quickly but also introduces the idea of partitioning and different ways of looking at numbers to make them easier to work with.
Then ask students to try with another set of numbers, 7 + 8 for example. Ask: What is 7 doubled? After they answer 14, ask: Now what is 7 + 8? If they don’t get 15, use the counters to get the answer and see the pattern of double and near double.
Partitioning simplifies math by breaking numbers into parts that are easier to work with. We often partition to give us numbers we can work with easily, like doubles or compatible numbers (up next), but you can partition numbers any way that helps you solve the problem.
For example, take 9 + 7. If you know that 9 + 1 = 10, you use partitioning. You partition the 7 into a 1 and a 6. You first add 9 and 1 to total 10, and then add on the 6.
You can use partitioning for subtraction, multiplication, and division as well as addition.
Compatible numbers add up to a “tidy sum,” or one that ends in zero, or multiples of 10.
Examples include 7 and 3; 9 and 1; and 6 and 4. When added, these number pairs add up to 10. Other examples include 30 and 70; 16 and 84; and 35 and 65, because when these numbers are added they total 100. Note that in all cases the numbers add up to a number ending in zero—a multiple of ten.
Students can use partitioning to create compatible numbers and then add on other numbers. Show students how to use these strategies together:
25 + 37 =
20 + 5 + 30 + 7 =
20 + 30 + 5 + 7 =
50 + 12 = 62
Or students might partition it this way to create compatible numbers:
25 + 37 =
25 + 25 + 12 =
50 + 12 = 62
Note that there are often multiple ways to partition numbers that can help students come to the same answer.
Estimating is a particularly important strategy because it allows us to judge how reasonable a responses is. Have you ever had a student come up with an answer that is way off? Sometimes this means students don’t understand the concept. Other times, they are just working too fast. Either way, estimating can help them decide whether their answer is reasonable. Make sure they understand that estimating is not exact—it won’t tell them if they are right, but it will tell them if their answer makes sense.
Estimating is more than guessing. Within this strategy, we have sub strategies, such as rounding, finding compatible numbers, and using benchmarks. Helping students learn the different ways to estimate will help them assess numbers in a variety of situations.
Fun activities to teach mental math
I’m always on the look out for easy and fun ways to help students practice mental math. Here are a few ideas.
Partition in pairs
Divide students into pairs. Give each pair a 100 grid. Each student selects a number from the 100 grid. Have students work independently to use partitioning to add the two numbers. Then have them compare to see if they partitioned the numbers in the same way. Have them explain their thinking to their partner.
Play count on cards
To play this game for 2 players you’ll need a deck of cards with the picture cards (Jack, Queen, King, Joker) removed. Separate the remaining cards into two piles, one with the cards: ace (acting as 1) to 4 and the other pile with the cards 5 to 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. Then have one student turn over the top two cards and add the two numbers using the counting on strategy. Remind them at the beginning of the game to count on from the larger number, and count on the smaller number. For example, if the two cards turned over were 8 and 3. They would start with 8, count on 3: 9, 10, 11.
If the player answers correctly, they get to keep both cards. If they answer incorrectly, the other player can try to answer the question to keep both the cards.
Then the other player takes a turn in the same way. Play continues until one of the piles run out of cards. The player with the most cards at the end of the game wins.
Set up a math station with a list of things to estimate. Use this as practice once you have taught students estimating techniques such as rounding, partitioning, and benchmarking. Have a list of things to estimate. Ask students to show how they estimated so that you know it isn’t just a guess. For example, you could have students estimate:
- how many blocks of the same size would fit in a particular box
- how many Mondays are in the school year
- the length of the room
- how many students are in the school given a list of class sizes (remind students to estimate instead of actually adding it up)
- how many words are on a given page in a book
If time permits, have students do the measurements or math to figure out the actual answers. How close were they? What could the do to estimate better next time?
For more activities for teaching mental math, plus a whole lot more, check out the Bumper Book of Fun Math Games and Activities. It’s no estimate—you get 138 pages of worksheets, games, and activities to assist in consolidating various math concepts. These activities are a mix of individual, small group, and whole class activities that are suitable for grades 1 – 4 and come with easy to follow instructions.