Compute Mental Math Chains – Elementary Math

Purpose

To engage in multi-step mental computation using all four operations

Materials

None

Overview

Read a mental math chain to students and ask them to mentally compute each step. Leave a slight pause between each step.

To keep students engaged, you can have them stand together and take one forward step for addition/multiplication and one backward step for subtraction/division. You can also use name cards to randomize who is selected to answer.

You may wish to play this game often to give students practice with mental computation. As the year progresses, you can adapt the length of the chains, the speed, and the complexity. These mental-math chains should always be given orally and not written because, if written and performed in this way, they may violate the rules known as “order of operations.”

About the sequence

Part 1 asks students to use addition, subtraction and multiplication to mentally compute multi-step problems with single digit addends, subtrahends and multipliers. In Part 2, the pace quickens and the chains lengthen, using all four operations. The extension progresses to include two-digit addends, subtrahends, multipliers, and divisors.

Part 1

Let’s make a number chain. Take one small step forward each time you add or multiply and take one step backwards each time you subtract.

Examples:

Start with 7, then add 3 (forward step), then subtract 5 (backward step), finally multiply by 2 (forward step) (= 10)
Start with 3, then add 8 (forward step), then subtract 4 (backward step), then multiply by 7 (forward step) and finally subtract 9 (backward step) (= 40)

While children are enjoying their building of mastery, feel free to repeat. When children are eager for more, try Step 2 or the extension.

Part 2

Let’s make another number chain! We’ll move a bit faster but we’ll stay in our seats this time and close our eyes as we mentally compute the next chain.

Examples:

Start with 9, then subtract 5, then multiply by 5, then multiply by 2, finally, divide by 5. (=8)
Start with 7, then multiply by 3, then add 4, then multiply by 4, finally divide by 5. (=20)

As always, when children seem excited for a new challenge, move on.

Extension

Now, let’s build a longer chain with bigger numbers.

Example:

Start with 21, then multiply by 2, then divide by 7, then multiply by 10, then subtract 3, then add 13, then multiply by 4 (= 280)