This is the earliest stage of understanding addition. Children count from one to find the sum. They often use manipulatives or count on their fingers.
For 5 + 2, a child will count, “1, 2, 3, 4, 5, 6, 7.”
Once your child is confident with doubles facts, he/she can be led to recognize doubles plus or minus one facts as close neighbors.
Students recognize that adding a single digit number to 10 means 10 and some more. This understanding helps children to use strategies to add double digit numbers with ease by using methods that involve place value splitting.
6 + 10 = 16
However, if a child has mastered ten facts, he or she could choose to manipulate other facts into ten facts.
8 + 5 = 8 +2 + 3
The 5 could be broken into 2 + 3. The 2 can be quickly added to 8 and now we have an easier fact: 10 + 3.
Students understand that it is faster to start with the larger addend and count on.
3 + 6 = 6, 7, 8, 9
Students come to recognize doubles facts as ‘numbers that have a partner’ on the number rack, or you can see them in a mirror. They should also notice that sums are always even. Committing these facts to memory will aid in the next strategy.
3 + 3 = 6
7 + 7 = 14
8 + 8 = 16
9 + 9 = 18
Begin to recognize “partners” of numbers that make 10. Since our number system is based on 10, when children are good at recognizing the combinations (i.e. 2 + 8; 4 + 6) they can begin to apply this to larger computation (i.e. 12 + 38; 24 + 17)
1 + 9
2 + 8
3 + 7
4 + 6
5 + 5
Since adding 10 to any number is ‘easy’, students quickly become comfortable seeing 9 as a next-door neighbor to 10. They can add 10 and then take 1 away. Or he/she can choose to take 1 from the other addend to ‘make the 9 into a 10’.
9 + 4 = 10 + 4 -1 = 13
Materials: dice and calculators
Use two dice. Roll the dice and say how many dots are on each die just by looking. Then add the number of dots. Enter the number into your calculator to keep progressive scores. The first person to reach a given number such as 100 wins. Variation: include three dice or dice of varying numbers, like a 4-9 die.
Materials: a pair of dice
Use two dice. Roll dice as many times as you like, adding the dots on the dice and keep a running total of the sum of your rolls. However, if you roll a 1 on one of the dice, your turn is over and 0 is scored for that round. If 1s come up on both dice, your turn is over and your total for the game thus far becomes 0. The first person to reach 100 wins.
Materials: a deck of cards
Deal out the deck of cards evenly between players. Face cards can be 10s or removed from the deck. Each player turns over the top two cards and adds them. The player with the larger sum takes all four cards. Variation: each player draws 1, player to announce sum first wins the match.
Variation for subtraction: the player with the larger number takes the two cards. They will also take as many beans or counters as the difference between the two numbers turned over (Ex: 6 and 4 are turned over, the player who turned over the 6 gets to take 2 beans).
Add difficulty: have each player turn over two cards each turn and add the sum of the cards.
Materials: a deck of cards
Use Aces as 1s and 2 – 9 from a deck of cards. Deal out 7 cards to each player. Place the remaining cards face down in the middle. Begin by players looking through their hands to see if they have matches, or combinations of 2 cards that will add to 10. Play begins as players take turns asking others for numbers they need to make a ten.
Variation: use flashcards or index cards with addition facts written but no answers. Matches/pairs are made by matching sums. (i.e. 3+ 2 and 4 +1 are a match). Players ask another for a sum for a card they have in their hand.
Materials: flashcards/index cards with addition facts w/o answers
Place the cards face down on a table or the floor in an orderly fashion. On each player’s turn, he or she turns over two cards and determines the sum on each card. If the sums are equal, the player has made a match and keeps the cards. (Thus, 8+1 and 3+6 can be a match.) If the sums are not equal, the two cards are turned back over and left in their same place.
Materials: 2 dice and paper
Each player writes 15 numbers using the numbers 1 - 9. Numbers may be used multiple times and not all numbers need to be used. The dice are rolled and the sum of the dice is determined. All players cross that sum out in any way possible on their lists. Thus, if you have the numbers, 1, 1, 1, 1, 2, 2, 2, 3, 3,5, 5, 5, 5, 6, 6 written on your paper and you roll a 7, you can cross out any combinations equaling 7. You could cross out 2 and 5; or 1, 3, and 3; or 6 and 1; etc. The game ends when one player crosses out all of his or her numbers or when no one can cross out a combination on their sheets.