Math Activity to Teach Doubling: Concentrating on Doubles

Game: Concentrating on Doubles
Strand: Number Sense and Numeration, Addition and beginning Multiplication
Math strategy: Doubling

Materials: 
Concentrating on Doubles cards ( BLM8 GEIM vol 5) 1 or 2 sets for each pair

Overview: 
Students can play in pairs or small groups. Similar to 'memory' or other concentration games, students place all of the cards face down and spread out on a desk or floor. Each player takes a turn, by turning up two cards at a time. The goal of the game is to match the doubles number expression with the correct sum card. If a match is found, the player keeps the cards. If a match is not found, then the cards are turned over in the same place, and it is the next player's turn. The player with the most matches wins.
*a variation on this would be to have students play individually with a timer to see how many matches he/she can find in a set amount of time.

How this supports Student Learning: 
This game provides opportunities for students to strengthen their doubles facts. Students are often able to learn certain number facts, such as doubles (e.g., 3+3 , 5+5) before others, and will use these known facts to derive answers for unknown facts (3+4 is related to 3+3 and 5+6 is related to 5+5). 
There are only ten double facts.  Students can practice learning facts by playing games such as concentrating on doubles, which will lead them to the learn the two times tables. The two times tables should be linked to student's prior knowledge about the addition of doubles.

Where to next?: 
This strategy is particularly helpful because students who know their two times table well can relate these facts to the three times table. If 2 x 4 is 8, then 3 x 4 is 8 plus one more group of 4.

They will see connections to everyday items when they think about doubles:

When students know the double facts (two times tables), they can apply this knowledge to the four times table by simply doubling the product.


Another way to help students learn doubles is by models. This helps students make connections between the models, the symbols, and the words. The emphasis is on understanding the concept and accessing the strategies for computations with multiplication.





Games to support where to next: 
Over-Easy Doubles GEIM Vol.5, pg. 73 (BLM10)
Snappy Doubles GEIM Vol.5, pg. 75 (BLM12)
Find a Friendly Neighbour GEIM Vol. 5, pg 75  (BLM13)
Spinning for Near-doubles GEIM Vol.5 pg 76 (BLM14)

Math Activity to Teach Doubling: Last One to School

Math Game: Last One to School
Strand:  Number Sense and Numeration - Multiplication
Strategy:  Doubling

This game is from the Number Sense and Numeration Guide to Effective Instruction K-3

Materials
• Last One to School game sheet (BLM11)
• 10 counters per player
• 1 ten-sided number cube (or a spinner on BLM4)
-recording sheet or whiteboard with dry erase marker

Overview: 
Students spin and record the double of that number removing a counter from the gameboard with that double.

How this supports student learning: 
Learning their doubles is the pre-cursor to multiplying by 2.  A strong knowledge of doubles will help support decomposing other facts into partial products and doubling these.  For example; to help solve 6 X 4 a student may use their knowledge that double 6 is 12 (2 X 6 = 12) and then double 12 is 24 to get the answer to 6 X 4=24  because 6 X 4 can be decomposed to 6 X 2 + 6 X 2.

Instructions:
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 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.

Where to Next?
Once students are in grade 2 the multiplication symbol is introduced.  Students can also record the multiplication fact which reflects the same addition fact.  E.g. 6 + 6 = 12  and 6 X 2 = 12
Playing a variety of games with doubling will help solidify this essential skill to develop multiplicative thinking.

Math Activity to Teach Doubling: Spinning for Doubles

Math Activity: Spinning for Doubles

Strand: Number Sense and Numeration, Addition & Multiplication
Math Strategy: Doubling

English:

French:

Materials:
• a copy of the board game and spinner
• counters, a pencil,
• a paper clip
• 2 players

Overview:
During this game students develop their understanding of the making doubles strategy as they work to find all the doubles needed to fill their game board. They take turns spinning the spinner; once the spinner stops, the student needs to identify what the double of that number is and place a counter on their side of the game board.  The players continue taking turns until one of them fills their entire game board.

How this Supports Student Learning: 
This game provides students an opportunity to practice learning their doubles.  Learning their doubles is an important milestone towards adding and multiplication.  Once students know their doubles, they can are quickly able to recognize near doubles and doubles plus one. This allows students to work with numbers flexibly, as they adjust numbers to make them easier to work with.

Where to next?
Concentrating on Doubles, Magic-Doubles, Over-Easy Doubles and Last One to School are all games that support the making doubles strategy. Practice with a variety of games will help the student to develop mastery of this strategy. Once the student is confident with making doubles you can introduce games that support the near doubles strategy, like Snappy Doubles, Find a Friendly Neighbour and Spinning for Near-Doubles.

These activities can be found, beginning on page 72, in the English Guide to Effective Instruction in Math Volume 5 https://bit.ly/2FNcQju and in the French Guide d'enseignement efficace des mathématiques, de la maternelle à la 6e année:Fascicule 5 on page 74-77 here.

Math Strategy: Doubling in Multiplication

Math Strategy: Doubling in Multiplication
Math Strand: Number Sense Multiplication 

Overview:

Students begin to use doubles in the early elementary years when learning addition facts. For example, students are doubling when they compute 3 + 3 = 6, 7 + 7 = 14, and 15 + 15 = 30. Soon they recognize that 3+3=6 is the same as 3 doubled (3 x 2)=6.

A situation where they may repeatedly add could be in a growing pattern.




As students begin to approach more involved math problems, they may accurately use repeated addition but the doubling strategy is more efficient.






Doubling can also occur when students see that a factor in a multiplication sentence can be broke into two equal parts:





The Guide to Effective Instruction in Mathematics Multiplication, Volume 3, page 23, has some information on doubling.

http://eworkshop.on.ca/edu/resources/guides/nsn_vol_3_multiplication.pdf



When students become aware of prime factorization they can use a more advanced form of doubling:



Note: The factors that work most effectively with doubling are 2, 4, 8, 16, 32...

How this supports student learning:

Through doubling, students are beginning to move away from addition and into multiplying. The nature of doubling promotes student thinking about the relationships between numbers.

WHERE TO NEXT?

In the younger years, promote the understanding of doubling when working with addition facts. Use terms like doubles, and two times the amount to connect to multiplication (Proportional Reasoning). Encourage students to use doubling in a ratio table to speed up the process when trying to find a term of a certain value. See if students can determine when doubling will not work in the different doubling situations noted above.


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