Math Fact Fluency
How can I help my child with their math facts?
What do we mean by "Fact Fluency?"
Fluency is...
Built on an understanding of numbers and the meaning of operations.
Learned by exploring patterns and properties.
Sequenced systematically to build on previously learned facts.
Not just about speed.*
Fact fluency also takes time to develop! Students need frequent and varied opportunities for strategic practice.
*Some research has shown that too much emphasis on speed can increase anxiety, which gets in the way of our ability to think. Also, while efficiency is a key part of fluency, being acccurate, flexible, and able to explain why things work are all important for future math success.
When is my child expected to be fluent? Fact Fluency in the Common Core
Addition & Subtraction
Kindergarten: Fluency within 5 (yellow facts on chart).
1st Grade: Fluency within 10 and +10 facts (blue facts).
2nd Grade: Fluency within 20 (remaining facts shown in pink).
Multiplication & Division
3rd Grade: Fluency within 100. Know all products of two 1-digit numbers, and use these to solve related division problems.
You can see that students have a lot longer to develop fluency in addition than for multiplication, and thus it's common for students to continue working on fluency in 4th and 5th grades.
How do we work on fact fluency?
Start with Self-Assessment
It's important for students to start by asking themselves:
What do I already know?
What do I still need to learn?
This helps students set goals and spend time on what they need.
This Factor Pairs tool is an online example of how 3rd-5th graders can self-assess around multiplication facts.
They can also make their own list on paper of "easy," "medium" and "hard" facts, or use color-coding to show that on one of these interactive charts:
Interactive Multiplication Chart
In the picture examples, I colored common "easy" facts in green. Yellow shows facts many kids have a pretty fast strategy for (e.g., skip counting by 2s and 5s). The facts left in white are often the hardest.
Use a Variety of Strategies for Learning New Facts
Often traditional flashcards and online games have students randomly practice all 100 facts at once, and as if they are unrelated. This does not build true fact fluency.
Using these strategies will help students make connections between facts and build number sense that will not only help them learn facts, but support their later work with bigger numbers and algebraic thinking!
Look for patterns.
Math is all about patterns! We can use patterns to help us remember facts and check our answers.
This is the 7th Standard for Mathematical Practice.
Use Facts You Know
The facts are connected, so students can use facts they know to learn ones they don't!
The clue cards below are one way to strategically practice new facts.
Set Specific Goals
Having a long list of facts to work on can feel overwhelming. Setting and achieving small goals can help.
Use the recommended order below to sequence goals.
Which facts should I work on next?
Use the recommended order below to help you decide what to work on next.
These facts build on each other in a logical way, and there are fewer facts to learn as you move through the levels, because of the commutative property (e.g., if you know 4x7=28, than you should also know 7x4)
Click on the links to see some visual examples you can talk about with your child. Ask them what they notice and wonder, and try out the same strategy with others numbers!
Addition & Subtraction
Foundational Facts:
Adding or subtracing one or two (e.g., 8+1, 15-1)
Adding and subtracing zero.
Make 5s (e.g., 2 + 3, 4+1)
Adding ten to a single digit (e.g., 6 + 10 = 16)
Doubles (e.g., 3+3, 9+9)
Make 10s (e.g., 9+1, 6+4)
Building on the Foundation:
Using make 10 facts (e.g., 9+7 = 9+1+6)
Using doubles (e.g., 6+7=6+6+1)
"Think Addition."
Once addition facts are known, students can use the relationship to solve subtraction facts. (e.g., when I see 8-5 I think 5+?=8 and I know 5+3=8, so 8-5=3!)
Multiplication & Division
Foundational Facts:
Doubles (e.g., 6x2) Students use the addition double facts they know!
Multiplying by 10 (e.g., 9x10) Count by tens and look at the pattern!
Multiplying by 5. Count by 5s, and notice the relationship to 10s facts.
Multiplying by 0 and 1. We don't start with these because having "groups of 1" and "groups of nothing" can be confusing, but usually easy to memorize. We want students to make sense of these facts too.
Building on the Foundation:
Multiplying by 3 and 6. Add one more group to your doubles to triple a number. (e.g., 2x7+7=3x7) You can add one more group to x5 facts to get x6 facts or double your x3 facts (e.g., 3x8=24, 6x8=24x2 or 48)
Multiplying by 4 and 8. Double your doubles, and then double again! (e.g., 2x3=6, 4x3=12, 8x3=24)
Multiplying by 9. These are one group less than the products of x10 facts (e..g., 9x4=10x4 -4)
Multiplying by 7. At this point students should actually know all of their x7 facts except for 7x7!
Making triangle cards is a great way to practice related addition and subtraction facts.
Cut a triangle out of paper and write two addends and their total in the three corners of a triangle. Circle the sum (or answer to an addition problem). Quiz a partner or yourself by covering one of the corners and trying to find the missing number!
(You can make triangle cards for multiplication & division too!)
Clue Cards
A twist on traditional flash cards, these "clue cards" have a "clue" or reminder to start with or think about something that will help the student find the answer.
Students can create their own personalized set of clue cards to work on their specific goals.
These cards emphasize the importance of mathematical relationships by:
reminding students of the commutative property of addition and multiplication (e.g., 3+6=6+3), rather than having them practice those two equivalent facts separately.
prompting students to use facts they know to find unknown answers efficiently.
To create a clue card like those pictured, simply write the two related expressions (e.g., 2 + 3 and 3 + 2 or 5 x 7 and 7 x 5) on the front of the card and the correct answer on the back.
It's often helpful for students to talk through what an efficient strategy for finding the answer might be in order to the "clue" on the front. Ask: "What other facts do you know that could help you find the answer to this one?"
