Double Facts
What is a double fact?
4 + 4 (any number that is the same)
What is a related fact? Think about the numbers 5, 8, and 13
Certain numbers and facts are related or make up a fact “family” and there are only three numbers in each family. They are related because you can add two of the numbers together to get the third number. 8 + 5 = 13. You can switch the order of the two numbers added above to equal the third number again. 5 + 8 = 13. You can also subtract the largest number from either the other two numbers to equal third number. 13 - 8 = 5 and 13 - 5 = 8.
Related Fact Family:
5 + 8 = 13
8 + 5 = 13
13 - 5 = 8
13 - 8 = 5
What is the Count Back strategy?
Count back 3
11, __, ___, ___
You count back the same number of times as the number you are subtracting
Count back 3
11, 10, 9, 8
Julie has 7 tickets to the football game. She buys 6 more. How many tickets does she have now? How far is the answer away from 10?
7 + 6 = 13
Double Fact: 7 + 7 = 14, one less OR 6 + 6 = 12, one more
13 - 10 = 3
Ben has 3 baseball cards. Jake gives him 9 more cards. How many baseball cards does Ben have now? Make a ten to solve the problem. Show your work.
3 + 9 = ?
10 + __ = ?
__ baseball cards
3 + 9 = 12
10 + 2 = 12
12 baseball cards
4 + 3 = ?
Double Fact: ___ + ___ = ?
4 + 3 =7
Double Fact: 4 + 4 = 8 or 5 + 5 = 10
How can you write related addition facts to solve the problem?
Mr. Weston picks 6 red flowers and 8 white flowers from his garden. How many flowers does he pick?
Create 2 different addition equations and solve (think about related fact families)
6 + 8 = 14
8 + 6 = 14
How many flowers does Mr. Weston pick: 14
Marie sees 15 fish in the river. There are 8 trout. The rest of the fish are catfish. How many catfish does Marie see? Write the subtraction problem. Then solve.
__ - __ = __
15 - 8 =
7 catfish
Paula records 5 songs. Then she records 6 more songs. She uses the doubles fact 5 + 5 = 10 and then subtracts 1 to find the sum. Explain the error Paula made. Then find the total number of songs she recorded.
5 + 6 = 11
5 + 5 = 10, one more
Paula's error was because she subtracts 1, not adds 1
There are 11 balloons in a bunch. Then Jackson and his family pop 8 balloons. How many balloons are in their bunch now? Show the tens fact you used.
10 - __ = ?
__ Balloons
11 - 8 = ?
10 - 7 = 3
11 - 8 = 3
3 balloons
8 + 9 = ?
Double Fact: ___ + ___ = ?
1 more or 1 less?
8 + 9 = 17
Double Fact: 9 + 9 = 18
1 less
OR
8 + 9 = 17
Double Fact: 8 + 8 = 16
1 more
What is the count on strategy?
9 + 4 = ?
Count on:
9, __, __, __, __.
You count on to add
9, 10, 11, 12, 13.
9 + 4 = 13
There are 10 cows in a field. 3 of the cows are brown. The rest of the cows are black and white. How many cows are black and white?
7 Black and White Cows
There are 9 ladybugs on a plant. There are 3 ladybugs on another plant. How many ladybugs are on both plants?
9 + 3 = 12
There are 4 blue pens, 5 red pens, and 5 black pens in a box. How many pens are in the box? Write an addition fact to show the problem. Write the sum.
____ + ____ +____= ?
___ pens
4 + 5 + 5 = 14
5 + 5 = 10
10 + 4 = 14
14 pens
9 + 8 = ? What double fact will help us solve this problem? Is the number one more or one less?
9 + 9 = 18 : One less : 9 + 8 = 17
Malik has 6 horse puzzles and 5 cat puzzles. How many puzzles does she have?
What mental addition strategy could you use to solve the problem?
6 + 5 = ?
Count on:
6, __, __, __, __, __
6, 7, 8, 9, 10, 11
11 puzzles
There are 7 green grapes and 8 red grapes in a bowl. Hw many green grapes are there? Use double facts to help you find the answer.
7 + 8 =
Double Fact: 7 + 7 = 14
one more
15 grapes
OR
7 + 8 =
Double Fact: 8 + 8 = 16
one less
15 grapes
Benjamin plants 5 trees on Saturday and 7 trees on Sunday. How many trees does he plant on the two days? Write an addition fact. Complete the bar model. Write a related subtraction fact. Solve.
5 + 7 = 12
On a bar model, the numbers 5 and 7 would be in boxes and the number 12 would be in the middle, under both boxes
There are 15 kayaks on the lake. There are 7 blue kayaks. The rest are red. How many kayaks are red? Use a number line to show how you can make a ten to subtract.
15 - 7 = ?
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
First, you start at 15, then hop back to the number 10. There are 5 hops between 15 and 10. Then from 10 you hop back to the number 7. There are 3 hops between 10 and 7. Then if you take 10 subtract 3 you get the number 8.
15 - 7 = 8
Colin has 7 marbles. He gets 6 more marbles from a friend. How many marbles does Colin have now?
7 + 6 = ?
Double Fact: ___ + ____ = ?
____ marbles
7 + 6 = ?
Double Fact: 7 + 7 = 14
13 Marbles
Complete the addition facts and a bar model. Then complete the related subtraction facts.
7 + 5 =
5 +7 =
12 - 7 =
12 - 5 =
7 + 5 = 12
5 +7 = 12
12 - 7 = 5
12 - 5 = 7
A bar graph would have two boxes, the largest labeled 7 and the second labeled 5. Under these boxes would be the answer to the combined addition numbers, so 12.
Kane counts 7 grasshoppers in the backyard and some grasshoppers in the front yard. There are 11 grasshoppers in all. How many grasshoppers are in the front yard?
Write an addition fact. Complete a bar model. Write a related subtraction fact. Solve.
11 = 7 + 4
11 - 7 = 4
4 grasshoppers
In a bar model the 7 would be in a bigger box, beside it would be a 5, then below the two boxes is the answer, 11.
Hank read 11 books. Karen read 3 books. Explain how to count back to find how many more books Hank read. Then solve the problem.
11 - 3 = ?
Counting back means you take the big number and count back the same number of times as the number you are subtracting
11, __, ___, __
11, 10, 9, 8
Jenna has 3 bags. There are 4 books in the first bag, 5 books in the second bag, and 6 books in the third bag. How many books does she have altogether? Explain how you solved the problem.
Double Fact: 5 + 5 = 10, one less
9 + 6 = 15
15 Books