TDSB Mathematics for Families & Caregivers

Using Near-Doubles

Overview

Using near-doubles is an addition and subtraction strategy. Students use their knowledge of double facts (eg. 4+4) to help solve the equation. Students use knowledge of doubles to solve addition and subtraction problems that are near known doubles facts.

Doubles are facts that have two addends that are the same. By familiarizing themselves with the doubles facts, students can efficiently use them to solve near-doubles problems.

Near-doubles are facts that have one added that is one more than the other addend. Students need to be comfortable with their doubles before they can attempt to use this strategy effectively.

Doubles and near-doubles appear in the addition & subtraction continuum. Doubling, a similar strategy, can be found on the multiplication/division continuum.

Examples of what students might do:

Marcus is faced with solving the problem:

9 + ⬜ = 16

Marcus states that he knows that 9 + 9 = 18; therefore if he starts with 9 and adds a number that is less than 9, the result will be 2 less than 18, or 16.

Since 9 - 2 = 7 the missing number is 7.

part-whole relationship

Marcus is deepening his understanding of the part-whole relationship of addition and subtraction. He knows that the number added to the first addend to get to the sum (whole) is the second addend.

Adapted from Alex Lawson What to Look For Resource. Pg 62-66

equivalence

Marcus also constructs the key idea of equivalence by adjusting both sides of the equation. He knows that, for addition, if he adds to or subtracts from an addend, then the same amount must be added to or subtracted from the sum to maintain equivalence.

Adapted from Alex Lawson What to Look For Resource. Pg 62-66

Marcus's thinking can be recorded to the left.

Marcus uses a double he knows to help solve the problem.

Note #1

There are only ten doubles facts from 0 + 0 to 9+ 9. These ten facts are a powerful tool to learn near-doubles facts.

Note #2

Near-doubles include all combinations where one addend is 1 more than the other. The strategy is to double the smaller number and add 1.

Note #3

Students who are using the known fact strategy are developing relational reasoning. They are beginning to work with numbers in more efficient and flexible ways, relying less on counting.

Note #4

Students are continuing to build on part-whole relationships, recognizing that a first number (or part), plus a count of the second number (part), will give them the total amount (whole).

Supporting Students with Using Near-Doubles

To ensure students grasp what is happening when they double have them build the amount with a concrete item, like snap cubes, and then double it.

Once students have automatic recall of their doubles facts they will be able to transfer this to solving questions with near doubles.

Use ten frames to help students visualize the learning.

When students are comfortable with their doubles facts, this will also support their understanding of multiplication tables.

For example, the two times tables (doubling 2’s) can then use these facts for the three times tables. For example, if 2x4 is 8, then 3x4 is 8 plus one more 4.

Games to Promote Using Near-Doubles

Concentrating on Doubles

Have students play individually or in pairs. Students place all cards face down and spread out on a desk or on the floor.

The players turn up two cards at a time. The object is to match the doubles number expression with the correct sum card. If a player finds a match, he or she keeps the cards. If the cards do not match, they are turned back over in the same place. Students working independently may want to use an egg timer to see how many matches they can find before the timer runs out. If playing in pairs, the player with the most matches wins.

Download the instructions and blackline masters for this game

Find a Friendly Neighbour

Have students work with a partner. Each player is dealt five cards. The remaining cards are placed face down in a pile. The object of the game is to create the most near-double matches.

On a turn, a player can put down any two cards that go in sequence (e.g., 7 and 8, 2 and 3, 4 and 5) and state the sum. That pair is then placed face up on the table as a matched near-double. If a player does not have a match in his or her hand, the player asks the other player for a card that would make a near-double.For example, if a player had a 7, he or she could ask the other player for a 6. If the other player has the card, he or she must give it to the asking player, who will then put the pair on the table and give the sum. If the player does not have the card asked for, he or she will say, “Try next door.” The asking player then picks up the next card from the face-down pile. Play ends when no more matches can be made.

The winner is the player who made the most matches.

Download the instructions and blackline masters for this game

Last One To School

Have students work with a partner. Each player takes 10 counters and places one inside each house on his or her side of the game sheet.

Once the counters have been placed, player 1 rolls the number cube (or spins) and says what the number showing would be when doubled. If that number house has a counter in it, the counter is moved to the centre of the game sheet in the “Last One to School” box. If a player rolls a number that has previously been rolled and the house is empty, that player misses his or her turn. Player 2 then rolls the number cube (or spins), doubles the number rolled, takes the counter from that numbered house, and places it in the centre of the game board.

The game continues until one player has successfully moved all his or her counters from the houses and sent all the students off to school.

Download the instructions and blackline masters for this game

Snappy Doubles

Have students work with a partner or in groups of four. Each player holds the 10 number cards face up in front of him or her.

Player 1 rolls the number cubes or spins the spinner. The other players look at their row of number cards to find the card that is the near-double of the number rolled or spun. For example, if the number 8 is rolled, players would be looking for the 9 card. The first player to snap his or her card on the table and state the near-double fact and sum correctly turns the card face down on the table. In this example, the player would snap the 9 on the table and say, “8+9=17”. Player 2 then rolls the number cube (or spins) for the players to match.

Play continues until one player has snapped all his or her cards face down on the table.

Download the instructions and blackline masters for this game

Spinning for Near-Doubles

Have students work with a partner.

Player 1 spins the spinner, doubles the number shown, and adds 1. If that space is available on his or her side of the game sheet, a counter is placed on that number. If a counter already occupies that space, that player misses his or her turn.

The game continues until one player has successfully filled in his or her side of the game sheet.

Download the instructions and blackline masters for this game

The Big Race

The Big Race is a game sheet that can be used to rehearse any of the addition or multiplication strategies in a paper-and-pencil format.

Each student needs a copy of the game sheet. Students will record in the centre box the one strategy they will use to complete the game sheet. Students will work their way around the game sheet by applying the strategy in the centre of the sheet to each number around the track.

Students will record their answer in the outer boxes on the game sheet.

This game is great for practising a strategy that is currently being taught, or for revisiting a strategy that has already been taught.

Download the instructions and blackline masters for this game

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