Mental math means solving mathematics problems in one’s head without using a calculator, pen or paper (piqosity.com).
It is not explicitly included in most curricula, so teachers may need to make time for it within ordinary number work (prodigygame.com). Use the prompts below alongside math games for children and focused multiplication practice. Ask students to share their thinking, and keep a written method available for checking.
Contents
1. Find each student’s starting strategy
Begin with one accessible calculation and ask the student to describe what they did first. Listen without supplying a method. Then offer a second question with similar numbers and ask whether they would begin the same way.
- Ask: “What did you notice first?”
- Probe: “What part did you work out?”
- Compare: “Is there another route?”
- Record: Note the words, drawings or jottings the student uses.
Use these notes when choosing the next example. Keep the conversation about the method as well as the answer.
2. Make ten first
Prepare pairs of number cards that can be combined to make ten. Show one card, then invite students to name a card that completes the pair. Move to addition questions only after students have had time to discuss the pairs aloud.
Use counters, fingers or a ten-frame when a visible representation is appropriate. Ask students to point to the part they would use first, then say the rest of the calculation in their own words.
Include questions with a larger whole-ten benchmark as a separate set. Keep the benchmark visible while students are first explaining their choices.
3. Partition by place value
Give a two-digit addition or subtraction question and invite students to say the tens and ones they notice. Provide paper for a temporary jotting, but ask students to explain each part before they write it.
Model one example by recording the parts in separate lines. Pause before combining anything and ask students what information each line represents.
Use a new question for partner talk. One partner can describe the partition while the other records the spoken steps, then they can compare their work with a written calculation.
4. Count on or back strategically
Present subtraction questions with different gaps between the numbers. Ask students to decide whether they want to count forward from the smaller number or backward from the larger number before they begin.
Offer an open number line for students who want to mark jumps. Ask them to label each jump and explain why they chose that direction.
Put two possible routes on the board without identifying a preferred one. Invite the class to compare the routes and check each result with a written calculation.
5. Build from doubles and near doubles
Display a known double and a nearby addition question. Ask students to identify the double they would start from and to state what would need to change.
Include questions on either side of the displayed double. Ask students to use a drawing, counters or a spoken explanation before recording an answer.
Collect two different explanations when possible. Keep both on display while students check whether each explanation matches the original question.
6. Compensate after rounding
Choose calculations that sit near a whole-ten benchmark. Ask students to identify the number they would adjust, the temporary calculation they would make, and the correction they would record afterward.
Require the adjustment and correction to be written as separate notes. Do not accept an answer until the student can connect both notes to the original expression.
Mix addition and subtraction questions in the same discussion. End by checking each answer through a written method or a second mental route.
7. Bridge through a benchmark
Write a calculation near a multiple of ten or one hundred. Before students calculate, ask them to circle the benchmark they notice and say how they might reach it.
Invite students to split a number verbally, then record their route with an open number line if needed. Keep the original expression visible throughout the discussion.
Offer a second question with a different benchmark. Ask students to explain what changed in their planning before they calculate.
8. Distribute multiplication
Give students a multiplication expression and ask them to describe a way of separating one factor into parts. Record each suggested part clearly before any calculation begins.
Invite pairs to make an area sketch or a written expansion that matches their chosen parts. Ask them to connect every part of the sketch or expansion to the original expression.
Use a written calculation afterward as a check. Keep discussion focused on whether the representation and the expression match.
9. Double and halve factors
Prepare several factor pairs and ask students to look for a pair they might reorganise by doubling one factor and halving the other. Have them write each version of the expression in a column.
Ask students to explain why a particular reorganisation looks convenient to them. If a proposed route is awkward, keep it as a comparison rather than treating it as an error.
Check the final result with a written method. Invite students to identify which expression they would choose next time and why.
10. Scale from known facts
Place one secure multiplication fact beside several related calculations involving place value. Ask students to state what they notice about the factors and to record their reasoning in words.
Use place-value charts or labelled grids when students need a visual record. Ask them to match each digit in the calculation to its position on the chart.
Include one calculation that students should check carefully rather than solve immediately. Discuss the checking method before collecting answers.
11. Use square-number relationships accurately
Use square-number relationships only when they are already part of students’ current mathematics work. Present one completed relationship and ask students to identify the numbers and operations shown.
Ask students to verify a proposed pattern with a written calculation or an area representation. Keep the original representation beside the verification.
When students suggest a shortcut, ask them to test it on another example before recording it as a class note. Avoid presenting a pattern as a rule without a check.
12. Revisit strategies through retrieval practice
Set a short, low-stakes mixed practice task in which students choose a strategy and note its name or describe it. Include questions from earlier lessons as well as current work.
Spaced practice distributes problems of the same kind across many sessions, while interleaved practice mixes different problem types rather than grouping them in blocks (Behavioral Sciences).
- Present a small mixed set.
- Allow quiet thinking time.
- Ask selected students to show or name their strategy.
- Discuss one error through a worked example.
For an error-analysis variation, present a flawed solution and ask students to work together to identify and correct it. Keep the focus on the calculation and the explanation rather than on speed.
