Your first grader can tell you that 3 + 5 is 8. Ask what 8 − 5 is, and many children start at 8 and count back on their fingers: "seven, six, five, ... three." They get it right, but slowly. Ask the same child about 8 − 3 and they start over. Nothing connects the two facts yet, so each one has to be learned alone.
Number bonds and fact families build that connection. A number bond shows that a whole is made of two parts. A fact family shows that the same three numbers make four equations: two additions and two subtractions. Once your child sees both, subtraction facts are no longer a second list to memorize. They are the same facts, run backwards.
What a number bond is
A number bond is a whole with two parts. Draw a circle at the top for the whole and two circles below it for the parts:
8
/ \
3 5The bond says that 8 is made of 3 and 5, and that 3 and 5 together make 8. Your child can read it both ways, and that matters. The bond shows how a number is built.
Children first meet bonds with small wholes. The bonds to 10 matter most: 10 is 6 and 4, 7 and 3, 9 and 1. Knowing them lets your child spot a missing part at a glance. If 10 is 6 and something, the something is 4.
What a fact family is
Take the bond 3, 5, 8 and write every equation those three numbers make:
- 3 + 5 = 8
- 5 + 3 = 8
- 8 − 3 = 5
- 8 − 5 = 3
That group is a fact family, and it shows two things. Adding the parts in either order gives the same whole, so 5 + 3 and 3 + 5 are one fact, not two. Subtraction also undoes addition: if 3 and 5 make 8, taking away 5 leaves 3.
Seeing the family gives your child three more equations from one fact they already know.
Common slips
Counting from one every time. The answer is right, but the method stops working as numbers grow. Ask your child to hold the bigger number in their head and count on, or to use the bond: "8 is 5 and 3, so 8 take away 5 leaves 3."
Turning the problem around. Some children write 5 − 8 for a problem that says 8 − 5, because they think the numbers can go in either order. Ask: "After you take some away, do you have more or fewer than 8?" The answer must be smaller than 8, and the bond shows which part is left.
Learning two facts for one family. Children who treat 3 + 5 and 5 + 3 as different facts have more to memorize than they need. Point out that the parts can swap places and the whole stays the same.
Ways to practice at home
You do not need flash cards to start. Use things at the table.
- Hide and find. Put 8 buttons or crackers in a cup. Show your child 5 of them and ask how many are under the cup. Then lift the cup to check.
- Bond to 10. Use 10 small objects. Split them into two groups under your hands and ask how many are hidden. Say the whole first, then the parts: "10 is 4 and..." Let your child fill the gap.
- Four equations. After any bond, have your child write the fact family or say it aloud. Read the four equations together and talk about what stays the same.
- Say it in a sentence. "Five and three make eight. Eight take away five leaves three." Saying both directions aloud links them.
Keep sessions short. Five minutes on one bond is a good session.
Words for a calm moment
When an answer is wrong, do not give it away. Ask which number is the whole: "Which number is the total? Is it one of the parts?" When your child gets one right, name what they did: "You knew 5 and 3 make 8, so you knew 8 take away 3 leaves 5. You used the family."
If your child is stuck, go back to a smaller whole and rebuild from there. Once 5 and 3 feel solid, 8 gets easier.
How SmartyPants Math fits in
SmartyPants Math's Grade 1 lessons today cover addition and subtraction word problems. The word-problem guide shows the five types of those stories and the mistake behind each. Read the word-problem guide, or see how the practice works.
References
- National Governors Association Center for Best Practices & Council of Chief State School Officers (2010). Common Core State Standards for Mathematics, Grade 1, Operations and Algebraic Thinking: 1.OA.B.3 (apply properties of operations, including that addends can be added in either order, as a strategy to add and subtract); 1.OA.B.4 (understand subtraction as an unknown-addend problem, for example subtract 10 − 8 by finding the number that makes 10 when added to 8); 1.OA.C.6 (add and subtract within 20, demonstrating fluency within 10).