Grade 3 • Mathematics • Basic Facts

Grade 3 Mathematics

Basic Facts

What is fact fluency?

Quick recall of basic facts is a focus of elementary mathematics instruction. The goal of instruction is to develop automaticity with basic facts. In other words, we want our students recall basic facts without occupying the mind with the low-level details required. They become an automatic response pattern or habit. It is usually the result of learning, repetition, and practice. Like driving a car or riding a bike, basic fact instruction is more complicated than simple memorization. 

The HCPSS approach to basic fact instruction is grounded in understanding developed by intentional lessons to explore meaning and patterns within a fact set. Students make use of strategies to find unknown sums and differences while working with repetition and practice to attain automaticity.  Facts are arranged in a deliberate sequence. 

Facts are organized by commonality. That is, facts are grouped by strategy or pattern. Multiplication and division within a fact set are taught together so that students can make connections between operations. There are fewer and fewer unknown facts as each new fact set is introduced.

• Doubles: These facts double. They multiply by 2. They divide by or have quotients of 2. They are naturally less difficult to learn for students.
• Tens: These facts multiply by 10. They divide by or have quotients of 10. They connect with ideas about skip-counting and have a distinct pattern. 
• Fives: These facts multiply by 5. They divide by or have quotients of 5. They connect with ideas about skip-counting and have a distinct pattern. The products are half of the related 10 fact. The quotients are double the related 10 fact. 
• Ones: These facts multiply by 1. They divide by or have quotients of 1. They have a distinct pattern. The products can be easy to recall because of the pattern. However, the representation of these facts (1 group of something) is rather abstract. 
• Zeros: These facts multiply by 0. They have quotients of 0. They have a distinct pattern. The products can be easy to recall because of the pattern. However, the representation of these facts (0 groups of something or groups of nothing) is rather abstract.
• Threes: These facts multiply by 3. They divide by or have quotients of 3. They can be thought of as tripling or x2 and 1 more group (i.e. 6 x 3 is the same as 6 x 2 and 1 more group of 6).
• Fours: These facts multiply by 4. They divide by or have quotients of 4. When multiplying by 4, we can double a factor and then double again. (i.e. 7 x 4 is the same as 7 x 2 and then 14 x 2).
• Sixes: These facts multiply by 6. They divide by or have quotients of 6. They can be though of as doubling a triple (which is already known). They can also be thought of as 5 times something and one more group (i.e. 6 x 7 can be thought of as 5 x 7 and 1 more group of 7).
• Eights: These facts multiply by 8. They divide by or have quotients of 8. They can be thought of as double, double, double. In other words, we can double a number 3 times to find the product of that number and 8. For example, 8 x 6 is the same as 2 x 6 (12) x 2 (24) x 2 (48).
• Nines: These facts multiply by 9. They divide by or have quotients of 9. One way to think of these facts is to think of a number x 10 and then 1 less group. For example, 9 x 8 is the same as 10 x 80 (80) and 1 less group of 8 (80 - 8 = 72).
• Last fact: If this sequence is followed, there is 1 fact remaining (7 x 7). It connects with learning about square numbers. Many of the strategies above can be applied to this fact.

Things to keep in mind:

• Understanding of operations must be in place before working on basic fact fluency.
• Fluency is developed over time. Teaching and practice should focus on targeted facts.
• Practicing basic facts should be quick, fun and engaging!

For more information:

Basic Facts Speed and Time Research Article Links to an external site.

Fact Cards by Quarter

Quarter 2 - x/÷ 2 Download x/÷ 2

, x/÷ 5 Download x/÷ 5

, x/÷10 Download x/÷10

x/÷ 0 Download x/÷ 0

, x/÷ 1 Download x/÷ 1

Quarter 3 - x/÷ 3 Download x/÷ 3

, x/÷ 4 Download x/÷ 4

, x/÷ 9 Download x/÷ 9

Quarter 4 - x/÷ 6 Download x/÷ 6

x/÷ 7 Download x/÷ 7

, x/÷ 8 Download x/÷ 8

 

Fact Card Games 

• Have an adult show you a flash card.  Give the answer as quickly as you can.

• Have an adult say a math fact leaving out one of the numbers.  Fill in the missing number.  (Example: 2 x ? = 6)

• Have an adult read aloud a multiplication fact.  You say the related division fact. (Example: 2 x 10 = 20 and 20 ÷ 10 = 2)

• Put one set of cards face down.  Each player takes turns flipping 2 cards.  When you find a related multiplication and division fact, you keep the pair. (Example: 2 x 10 = 20 and 20 ÷ 10 = 2)

• Say each flash card aloud with a parent before you go to bed.

• Use a manipulative (macaroni, beads, buttons) to show each math fact.
• Play Memory by using 2 sets of cards and putting them face down.  Keep the matches you find.
• Play Compare by splitting the fact cards into two piles. Each player flips a card over, and the player with the greater product/quotient keeps both cards.
• Pick a fact card and draw a picture to show the fact.
• Write a word problem to go with a fact.  Solve your problem.  (Example: 3 x 2, "There are 3 snack bags with 2 cookies in each bag. How many cookies are in the snack bags?")
• Spread out all or some of the fact cards on a table. Say a product/quotient and have your child find the fact card that goes with it.
• Tape fact cards on different doors in your house. Have your child give the product/quotient for the fact card before being able to open the door.

Vocabulary

*Fact Family: a collection of related addition and subtraction facts made from the same numbers (Example: For 3, 5, and 15, the addition/subtraction fact family consists of 3 x 5 = 15, 5 x 3 = 15, 15 ÷ 3 = 5, 15 ÷ 5 = 3)

*Factor: a number that is multiplied by another number to get a product
*Product: the result of multiplication 

*Dividend: a number that is divided by another number
*Quotient: the number, not including the remainder, that results from dividing