Doubles Plus One & Near Doubles - First Grade Mathematics
Once you have mastered your doubles facts (like 4 + 4 = 8 and 5 + 5 = 10), you possess a secret key that unlocks many new addition facts! In mathematics, problems like 4 + 5 or 6 + 7 are called near doubles or "doubles plus one" facts. Why? Because the two addends are right next to each other on the number path. Instead of counting on your fingers one by one, you can think of the known doubles fact and simply add one more to find the total. In this chapter, you will master the doubles-plus-one strategy and use your doubles superpowers to add within 20 in the blink of an eye.
What Is a Near Double?
A near double is an addition problem where the two addends differ by just one unit.
The Anatomy of 4 + 5:
Look at the Addends: 4 and 5
5 is just 4 + 1!
So 4 + 5 is really: [ 4 + 4 ] + 1
\_____/
8 + 1 = 9!
Building Near Doubles with Connecting Cubes
Imagine building two towers side by side:
Tower 1 has 4 cubes: [#|#|#|#]
Tower 2 has 5 cubes: [#|#|#|#|#]
Notice that Tower 2 is an exact twin of Tower 1, with just ONE extra cube peeking out on top! If you know the two twins equal 8 (4 + 4 = 8), adding that single extra cube gives 9.
The Doubles-Plus-One Facts up to 20
Let us walk through the most famous near-doubles facts and see how they connect to their doubles anchors.
The Near-Doubles Reference Table:
Problem Think Double Add 1 More Sum
1 + 2 1 + 1 = 2 2 + 1 3
2 + 3 2 + 2 = 4 4 + 1 5
3 + 4 3 + 3 = 6 6 + 1 7
4 + 5 4 + 4 = 8 8 + 1 9
5 + 6 5 + 5 = 10 10 + 1 11
6 + 7 6 + 6 = 12 12 + 1 13
7 + 8 7 + 7 = 14 14 + 1 15
8 + 9 8 + 8 = 16 16 + 1 17
9 + 10 9 + 9 = 18 18 + 1 19
Notice the Sums: Always Odd!
In Unit 3, you learned that every double fact always equals an even number. When you add 1 to an even number, what do you get? An odd number! Every single doubles-plus-one sum is an odd number: 3, 5, 7, 9, 11, 13, 15, 17, 19.
Doubles Minus One: The Alternate Thinking Way
You can also think of near doubles by starting with the bigger double and subtracting one!
Solving 6 + 7:
Way 1 (Doubles Plus 1): Double 6 is 12, plus 1 is 13!
Way 2 (Doubles Minus 1): Double 7 is 14, minus 1 is 13!
Both ways lead to 13!
Choosing Your Favorite Anchor
Some mathematicians prefer building up from the smaller double, while others prefer stepping down from the larger double. Both ways show flexible mathematical thinking!
Practice Exercises
Exercise 1: Solve 5 + 6 using the doubles-plus-one strategy. Name the double fact you use as your anchor, and explain the steps to find the sum.
Exercise 2: Solve these near-doubles problems mentally: 3 + 4 = __ 6 + 7 = __ 7 + 8 = __ 8 + 9 = __
Exercise 3: Why is the sum of a near-double fact always an odd number?
Exercise 4: Explain how you can solve 7 + 6 using the turn-around rule and the doubles-plus-one strategy.
Solutions and Explanations
Solution to Exercise 1: To solve 5 + 6, think of the double fact 5 + 5 = 10. Since 6 is one more than 5, add 1 more to 10: 10 + 1 = 11. The sum is 11.
Solution to Exercise 2: 3 + 4 = 7 (Double 3 is 6, plus 1 is 7) 6 + 7 = 13 (Double 6 is 12, plus 1 is 13) 7 + 8 = 15 (Double 7 is 14, plus 1 is 15) 8 + 9 = 17 (Double 8 is 16, plus 1 is 17)
Solution to Exercise 3: A doubles fact combines two equal amounts, which creates pairs and always equals an even number. When you add 1 extra unit to an even number, that extra unit has no partner, resulting in an odd number.
Solution to Exercise 4: First, use the turn-around rule to rewrite 7 + 6 as 6 + 7. Then use the doubles-plus-one strategy: double 6 is 12, and 12 plus 1 is 13.