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Mental Math

Mental Math exercises (the Skills Practice & Review) are lively, brief, highly focused, and daily.

They are strategically selected to

  • build students' mental math skills quickly
  • increase their capacity to hold multiple pieces of mathematical information in their head simultaneously and
  • build their algebraic intuitions so that they have properties of operations, as well as full fluency with facts, to help them compute.These are very short and highly focused drills, spaced out over time (a few minutes a day rather than aggregated into a single lesson), because learning-research has long known[1] that that is the most effective approach.
  • Most times these are verbal exercises with the whole class; sometimes they take other formats.

Because the exercises are focused, not random, students build ways of thinking about computation as well as fluency with the facts, and gain competence very rapidly. These exercises are intended to be lively, with no instruction “wrapped around” them, and students typically enjoy the pace and the competence they gain.

Conducting the exercise

At the beginning of the lesson, the teacher tells students what the exercise is. For example:

  • Teacher: “Today, we're making pairs that add to 100. If I say, for example, 'forty,' you say 'sixty.' Ready? Eighty.”
  • Student: “Twenty”

After the introduction, keep words to a minimum. Give a number as a "prompt." Students answer with a number. That's it! No more words than that! Reducing the words to pay attention to actually increases the attention focused on the mathematical pattern.

Variations and management

Often these are done orally with the whole class.

Sometimes physically active engagement will be suggested. For example:

  • Students may write responses on personal white boards and hold them up for the teacher to see.
  • In slightly more varied exercises, you may create a table on the board with missing values. Four or five students at once come to the board to fill in any part of the table they choose, and hand the marker to other students when they finish.
  • You may draw a number line on the board along which students, again, several at once, place and rearrange numbers.

Varying the style occasionally keeps the activity feeling fresh.

  • You might have the class call out answers, letting everyone participate without raising hands. Advantages: energy and liveliness, the number of students getting practice, and the amount of practice they get (because many will answer each problem, rather than only when they get called). Disadvantage: potential loudness and students who don't respond.
  • Or select students by name to involve students who might otherwise sit back. One way is to keep a deck of 5x8 cards with students' names printed large and in bold so that they are READABLE from their seats. LET STUDENTS WATCH FOR THEIR NAMES (rather than listening for you to call them). Your voice conveys only the problem. Their eyes must be alert for who is to answer. Advantages: more control for you; greater visual attention for them. Disadvantage: less practice per student.
  • Or a bit of both: if students are arranged in rows or at tables, select a row/table at a time and let all answer. That way, many students do the problem at once, but not all, making it easier for you to see who's "hanging back."
  • Or select students alternately to give prompts and to respond. E.g., for the rule given above, one student says "eighty" and the next says "twenty." This encourages students to notice what rules govern the posing of the problem. In this "pairs-to-100" exercise, for example, giving a prompt of "24" is a playful challenge (or a misunderstanding of the rules) when people are expecting powers of 10.
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