Basic Facts for addition and multiplication refer to those combinations where both addends or both factors are less than 10. Subtraction and division facts correspond to addition and multiplication facts. Thus
15-8=7 is a subtraction fact because both parts are less than 10.
In order to master basic facts children need to construct efficient and effective mental tools to help them. The strategies found below will help children develop these tools.
A general approach to teaching basic facts through strategies includes:
1. Introduction of a strategy
2. Practicing the strategy
3. Adding new strategies
4. Practicing strategy selection
Vocabulary: Addends, Sum, Fact Family, Turn Around Fact
Facts with Zero
19 facts have zero as one of the addends
NEED: rope with knots, hopscotch if desired or numbers to tape to floor.
Use rope with knots: One end is 0 and the other end is 10. Have students start on one number then you say +1, +2 or +0 and see what happens. point out that at +0 the student doesn't move.
Same idea can be carried out with hopscotch or numbers taped on floor. Children hop forward O, 1, or 2.
Used when one addend is 1, 2 or 3. Why not with higher numbers?
· Use rope from above and add counting on or use number
· Put big number in your head and then count on. Model with pictures on overhead
· Use spinner for choral response
NEED: transparent spinner with 1 more, two more, +1, +2...overhead cards 4-9.
Use spinner with one more and two more. Pull card from deck of 4, 5, 6, 7, 8, and 9. After roll children should say 4 and 2 more are 6.
There are 10 doubles facts from 0+0 to 9+9
NEED: Two of Everything, mirrors, beans, pictures to coincide with doubles, large sheets paper for teacher pictures, doubles pictures, calculators
Have teachers brainstorm at tables and prepare poster for doubles. Take few minutes to share.
Use book Two of Everything.Let children place certain number of beans in front of them and them put mirror in front. Since mirror gives reflection, it actually shows double. Have children record doubles fact and what they see in mirror.
· Have children construct doubles anchor chart
· Calculator doubles: Use calculator to enter doubles maker 2 x1=2 then enter any number and decide on response if this number is doubled. press = and check response. Enter another number (no need to reenter 2X)
Doubles Plus 1 (also known as Near Doubles)
Includes all combinations where one addend is one more than the other. The strategy is to double the smaller number and add 1. Be sure children understand the doubles strategy before starting this strategy.
· Have children model double: 2 red bears plus two red bears. Then add green bear to one side. Have them pick out hidden double.
· Give children set of dominos and ask them to pick out doubles, doubles + 1 and then choose two to write about. Good for assessment
PRACTICE STRATEGY SELECTION
· Roll dice and put under correct label: doubles, doubles plus one , zero or counting on
NEED: Two die per set of teachers (give with # and dots), dominos depending on age of children and conceptual understanding, give 2 dice (# or dots) roll 2 dice... use recording sheet labeled DOUBLE, DOUBLES +1,Zero Fact or Counting on
Children roll 2 dice and decide if it represents a double, double +1 etc.
Children take turns until they have rolled 25 times. Each time they should record problem under correct column. They should tally how many of each were rolled.
Make a Ten
Used when one of the addends is 8 or 9
· Use large ten frame on ground and have children step on it and model.
· Then, have children use ten frame and model with partner
Need: Visqueen Ten Frame, paper plates for large ten frame, one die with all 8s and 9s and regular die individual ten frames
Facts for Ten (Ten Frame Facts)
These include facts that add to 10.
Read Ten Black Dots
NEED: ten frames with dots, blank overheads, vis a vis marker, overhead ten frame and markers, decks of cards- 1 per pair, overhead cards (A-9), ten frame on visqueen
show ten frames and have children tell how many without counting. Then challenge them to tell how many more are needed to make a ten. Record on overhead their responses. Use children in place of beans.
Use only ace-9 cards (ace =1). Shuffle in place turned over on desk. Turn top card over. Each student takes turn turning over card. If he she can make a ten, using two cards, he/she gets to keep the cards. Next player turns over card. If can'y make a sum of ten, card stays on desk and play continues to next person who flips card and tries to make a 10 with any of the cards showing.
PRACTICE STRATEGY SELECTION
· Two Dice Bump, Three Dice
· 4x4 Sum
Ten Plus Facts (by definition not a basic fact, but like to include)
These are addition problems where one addend is a ten.
NEED: double ten frames on overhead, overhead markers of two different colors.
Model 10 +6 on overhead and several other 10+ facts. have children determine how alike and how different.. Have them generate rule for adding numbers to 10.
Make a Ten Facts
These facts have at least one addend of 8 or 9. The strategy is to build onto the 8 or 9 up to 10 and then add on the rest. For 6+8 think: start with 8 and 2 more makes 10 that leaves 4 more so the answer is 14. Before using this strategy make sure children have been practicing thinking of numbers such as 11 as 10 and 1 more or 18 as 10 and 8 more.
NEED: double 10 frames on visqueen, double ten frame on overhead and one per participant
choose a fact with 8 or 9 as addend; 8+4. Have 8 stand on one 10 frame and 4 on the other. Ask children what could be dome to make this problem easier and build on something they know.
As practice for all strategies:
Place problems on overhead and have children discuss among themselves which strategy they would use and then discuss as whole class.
In sets by strategies, make cards that have number on one side and answer on the other. For example, 2 and 4, 3 and 6, 4 and 8. have children pass through "function box" When they come out on other side have students tell what happen to the number they went in with. record as each enters and exits under in and out. Do for doubles, doubles plus one, zero, one more, two more
Other Strategies and the Last 6 Facts
The above 5 strategies account for 88 of the 100 basic facts. The remaining 12 are really only six facts and their respective turn arounds.
Doubles Plus Two or Two Apart Facts
Of the remaining six facts, three have addends that differ by two. There are two approaches:
o some children extend the knowledge of doubles plus one to doubles plus two 4+6 is double 4 plus two more which equals 10.
o others take one from the larger addend and give it to the smaller addend. Thus the 4+6 fact becomes the double 5 fact (give one from the 6 to the 4) which equals 10.
Make Ten Extended
Three of the six facts have 7 as one of the addends. Often the Make A Ten Strategy is extended to these facts. Thus for 7+5, think 7+3=10 and 2 more is 12.
Counting on is taught as a strategy for all facts that have a 1, 2, or 3 as an addend.
Subtraction as Think Addition
The child uses known addition facts to produce the unknown quantity or part. For 9-4 think: 4 + ? is 9. This strategy is appropriate for subtraction facts with sums of 10 or less.
Facts with Zero
This set includes those involving minus zero (7-0) and those with a difference of zero (7-7).
One Less Than, Two Less Than
This group includes all facts with differences of 1 or 2 (8-7, 8-6) as well as those that involve -1 or -2 (8-1, 8-2). When teaching this strategy, frequently follow one fact with its partner. That is, follow 9-2 with 9-7 and discuss how these facts are alike. Then write the 7+2=9 fact. Help children see how the two more than and two less than relationships are involved in both facts.
Ten Frame facts
This group includes all facts with the first number of 10 (10-7), those involving -5 (8-5) and those with a difference of 5 (8-3).
Doubles and Near Doubles
This group refers to the addition facts of the same name. For 12 - 6 think: 6+6 =12. 9
For 9-4 think: 4+4 = 8 and 4+5 =9 so 9-4+5.
Picture a Ten Frame. Take one away and add on the extras. For 15-9 think: 15 equals one ten frame and 5 more. Take nine off the ten frame and you have 1 in the Ten frame plus the 5 left over = 6.