Primary Math//Addition & Subtraction Strategies
Addition Strategies in Primary
Based on Carole Fullerton’s “Mastering the Facts: Addition“
It is great making real life connections with math, through math story books (One is a Snail, Ten is a Crab) as well as using objects to relate to numbers (I have 3 teddies and I got one more for my birthday, how many do I have?) as well as using numbers as money talk (I have 5 dollars, if I had double that amount, how much would I have?)
Plus 1 (adding 1)
- We can count on from any bigger number. When we say the number that comes next, we are adding one.
- Students enjoy singing the Sharon, Lois and Bram (French/English) song “One elephant, deux éléphants”
- When we add the same amount twice, we make a sum that is double.
- We make connections to doubles around us in the world and imagine them to help us remember.
- 3+3 (legs on a lady bug)
- 4+4 (legs on a spider)
- 5+5 (fingers on each hand)
- 6+6 (eggs in a carton)
- 7+7 (2 weeks on the calendar)
- 8+8 (crayons in a crayola box of 16)
- 9+9 (wheels on a semi)
- In English we can make rhymes to remember as well
- 3+3 is 6, that’s a lot of sticks!
- 4+4 is 8, hurry we can’t be late!
Presque Doubles (Near Doubles)… better known as doubles + 1
- For the near doubles, we find the closest double fact then add one more.
- Students search for neighbours: 6+7 or 3+4
- Double the SMALLER number and add 1
- Alternatively, students can double the bigger number and subtract one as well.
Les Amis De 10 (Make 10 or also known as Ten Friends)
- We can “see the parts of ten” by using a ten-frame
- When a ten frame is filled to 7, the student notices that there are 3 empty spots: 7+3=10!
- In the classroom we have a rainbow and on each end of the rainbow are the complimentary numbers. (ROYJBIV) On the red bow there will be 0 on one end and 10 on the other, on the orange bow there is 1 on one end and 9 on the other. WHen the complete rainbow is formed the numbers 0-10 as displayed and is a quick visual for the students who need it. Google: 10 friends rainbow
- 0+10… 10+0
- 1+9… 9+1
- 2+8… 8+2
- 3+7… 7+3
- 4+6… 6+4
Plus 10 (add 10)
- It’s easy to add tens!
- The “ten and” facts are the teen numbers (but in French a bit more complicated)
- We use a full ten frame and a part ten-frame (ten and some more), as well as place value tent cards to help us visualize the place-value concept: that the 1 in 13 means ten
- To print at home: adding ten tents
9+ et 8+ (bridge through 10)
- When we add 8 and 9 we want to use the friendly number 10 once more.
- We compensate (take one and give to another) when we deal with +8 and +9
- Students take (subtract) 2 from other number so that the 8 becomes 10 and continues the addition. ex: 8+4 …. (4-2= 2, 8+2=10) 10+2= 12
- Students take (subtract) 1 from the other number so that 9 becomes 10 and continues the addition. ex: 9+6 … (6-1=5, 9+1=10) 10+5=15
Plus 2 (add 2)
- Adding on is continued in the add 2 strategy just like in +1
- Students should be able to count on two without the use of their fingers very quickly once they get a beat of two in their head.
- For practice: Roll a 6 (tap, tap) 8…6+2=8
La Scie (the “two aparts” or the “in-betweens”)
- We continue with compensation in this strategy (take 2 from one, give 2 to the other)
- When we add numbers that are two apart we are able to take 1 from the bigger number and give 1 from the smaller number to make a DOUBLE!
- 3+5… 5-1=4… 3+1=4… 4+4=8!
- Once student get quick and see the concept with counters they can skip ahead and see that numbers are two apart and double the number that comes in between.
- 6+8… 6-7-8… 7+7=14
Les 2 Derniers (the last 2 facts)
- Womp womp, the lonely 2 (and their inverse)
- 6+3 and 7+4
- We can use our knowledge from all the other facts to help up with these last two.
- If we know that 6+2 is 8, 9 is one more
- If we know that 7+3 is a 10 friend then one more is 11
Subtraction Strategies in primary (to 10)
Based on Carole Fullerton’s “Mastering the Facts: Subtraction“
Students will masters subtraction facts over grades 1-3.
In Grade 1 students are introduced to the idea of subtracting as removal and comparison.
Soustraire Les Doubles (Get to Zero: Subtract The Doubles)
- Subtracting ALL: Start with 4 take away (all) 4 left with nothing: 4-4=0
- We take away as many counters as we started with
- Create stories where student get to zero: I had 10 dollars and I spent it all! How much do I have left?
Un De Moins (One Less)
- Counting down by 1
- Using a number line show one jump backwards, taking one counter away, or by using the subtraction symbol.
- When we subtract by one we say the number that comes before.
- Game: roll a dice (6, 10, or 12 sided) and say “3! 3 take away one is 2!” (en Francais: 3! 3 moins un égale 2!)
- Create stories where students take away one: I had 5 candies and my brother ate one. How many candies do I have left?
- Pete the Cat and His Four Groovy Buttons : He looses his buttons ONE at a time! Perfect!
Moins 2 (Two away: Take Away 2)
- Start with even numbers which helps with counting backwards by 2s
- Number lines help show two jumps backwards
- Play the game from One Less but this time take away 2.
Stop here! The goal is that your child has a response in 3-second for these 3 facts.
Les Voisins (The Neighbours)
- Numbers that are “next door” are right next to each other. Their numbers differ by 1. One number is one bigger than the other.
- The difference between 9 and 8 is one. 9-8=1. La différence entre 9 et 8 est 1.
- This strategy is to allow students to see numbers in a row vs counting down or taking away the smaller number (9 counting down 8 to 1).
- Students might find the answer by counting up.
- Game: flip two dominoes, if the dominoe is a neighbour say the subtraction sentence (5-4=1: Neighbours!) (5-4=1: Voisins!) and keep both. Take turns and whoever has the most dominioes in the end wins.
Les Presque Voisins (The Near Neighbours)
- Add up to find the difference between numbers that are 2 away
- Students will come to decide that counting up by 2 is easier than counting back by 5 (7-5=2) and later decide in problems which strategy to use
- Game: have X number of counters and cover up all but two. How many are hiding? Record equations: (example) 10- ____ = 2
Les parties de 10 (Parts of 10)
- Les Amis De 10 (Ten Friends) in subtraction
- With ten frames students see the missing part. Ex: 8 on a ten frame has 2 empty squares: 10-8=2
- Using ten frames, have students come up with the equations of 10- ___=___
- Use word problems: I had 10 freezies and 6 melted, how many are still frozen? How do you know?
Moins 5 (Take Away 5): Ten Frame strategy
- Students need to use a ten frame in order to visualize the 5 being taken away (which is the full top row of a ten frame)
- Equations will be with numbers bigger than 5: for example 8-5 or 6-5
- As we go along students are able to use multiple strategies to find the answer. For example 7-5 is a take away 5, as well as a Nearly Neighbours. The goal in the end is to not count back 5 but instead to use the most efficient strategy.
- Use word problems (and draw them out!): My sister has 9 teeth and lost 5 of them, how many teeth does she have left?
Arbre de Soustraction (Subtraction Family Tree)
- How can 9 apples be in two trees? 8/1, 7/2, 5/4 etc
- If we can see how many apples are in the one tree but not the other and we know there should be 9 all together, how many are in the hidden tree? (Ex: 9= __+5 or 9= 4+____) then move onto 9-5=___ how do you know that?
- When we subtract we are looking for the missing part. We make connections to what we know in addition to find the missing part in subtraction.
- Subtraction Tree (Arbre De Soustraction) are the number families that are all represented together: 9-3= 6, 9-6=3 as well as their addition counterparts.
If we have time// A little challenge before grade 2
Moins 10 (Take Away 10): Facts to 20
- By using two ten frames: one full (10) and the other part (1-9) the students see the visual representations of taking away 10 and seeing how many is left.
- The digit in the ones (unités) stays while the tens (dizaines) gets taken away.
Moins 11 (Take Away 11): Facts to 20
- Just like Moins 10 (Take Away 10) students need to think of taking away ten and one more