2-Digit Mental Mathematics

Strand: Number
Outcomes: 6 and 7

Step 5: Follow-up on Assessment

Guiding Questions

What conclusions can be made from assessment information?
How effective have instructional approaches been?
What are the next steps in instruction?

A. Addressing Gaps in Learning

Students who have difficulty with mental mathematics strategies may have gaps in their understanding of number. They may need more experiences with counting. Visual materials like ten frames may help them to develop the number sense they need to perform mental calculations. Activities involving dice or cards can also help build meaningful associations between representations of numbers and actual quantities. Having students practise mental mathematics skills using smaller numbers, e.g., numbers to 20, while developing understanding of larger
2-digit numbers, can help develop fluency.

For example:

Ask students who are struggling with questions, like 42 + 37, to solve similar problems with smaller numbers, like 12 + 17.
Photocopy sets of tiny ten frame cards with several tens included in each set. Students can use these to illustrate solutions to mental mathematics questions or to make up 2-digit equations for each other to solve.
Allow students to use a calculator to perform or check calculations some of the time. Have them predict outcomes before entering anything into the calculator. Encourage them to break numbers up in different ways and add or subtract the pieces.
Allow students to use ten bars and unit cubes to illustrate mental mathematics calculations.
If available, use an arithmetic rack with 100 beads to illustrate student's thinking during discussions. Individual student arithmetic racks (also called rekenreks) with 100 beads also exist for students to use as visual models of mental mathematics.

B. Reinforcing and Extending Learning

Students who have achieved or exceeded the outcomes will benefit from ongoing opportunities to apply and extend their learning. These activities should support students in developing a deeper understanding of the concept and should not progress to the outcomes in subsequent grades.

Consider strategies, such as the following.

Have students organize a mental mathematics competition or computation "bee." They will need to write 2-digit addition and subtraction questions on cards, and calculate the correct answers. The teams or individuals with the most correct answers will win. There can be a time limit for each question, but speed should not be the goal.
Teach alternate subtraction strategies, such as cancelling out common amounts to make the question simpler (e.g., take 50 away from both numbers in the equation 77 – 58 = ? to make 27 – 8). Another strategy is the principle of constant difference. For constant difference, students add or subtract the same amount from each number in a subtraction equation, knowing the answer won't change. Instead of solving 97 – 59 =? they can add three to each number to create the question 100 – 62, which is much easier to solve.
Encourage students to play more complex, challenging games. For example, in the game "Closest to 100," two people play with a regular card deck that has had the tens and face cards removed. Each player gets six cards in their hand. From these cards they need to select four cards to make two 2-digit numbers that add up to a number that is as close as possible, or equal, to 100. The difference between their number and 100 is their score for that turn. The cards that have been used are discarded and each player gets four more cards. Play continues until the deck is used up. Players add up their total score. The player with the lowest total wins.

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