ILLINOIS TEACH & TALK

Create easier known products:

A teacher may ask students to solve 3 x 4=12 Students could then show how they think about 3 x 4 in order to get 12. 

 

Next the teacher may ask students to solve 3 x 5=15 students can show the various ways in which they think about 3 x 5 to get 15. 

 

Finally, the teacher can ask students to solve 3 x 9.  The teacher may point out that they could use the information on the board in order to solve 3 x 9.  Hopefully, students could see that (3 x 4) + (3 x 5) is the same as 3 x 9.  A way to prove this would be to draw a picture. 

 

By practicing these kind of multiplication warm-ups students will have the tools and strategies to solve any multiplication problem that is one-digit by one-digit.  In terms of fluency, students will have a strategy they can use that works for them in order to get an answer versus just memorization and then being stuck because they do not know the fact.  

 

The Grade 3 Flipbook has a good definition of fluency and how it applies to 3rd graders and multiplication. 

This standard uses the word fluently, which means accuracy, efficiency (using a reasonable amount of steps and time), and flexibility (using strategies such as the distributive property). “Know from memory” does not mean focusing only on timed tests and repetitive practice, but ample experiences working with manipulatives, pictures, arrays, word problems, and numbers to internalize the basic facts (up to 9 x 9). Multiplying and dividing fluently refers to knowledge of procedures, knowledge of when and how to use them appropriately, and skill in performing them flexibly, accurately, and efficiently.

 

Kansas Association of Teachers of Mathematics (KATM) Flipbooks. 

Questions or to send feedback: melisa@ksu.edu. Retrieved from Math Flipbooks.

 

Other Strategies to attain fluency include:

• Multiplication by zeroes and ones

• Doubles (2s facts), Doubling twice (4s), Doubling three times (8s)

• Tens facts (relating to place value, 5 x 10 is 5 tens or 50)

• Five facts (half of tens)

• Skip counting (counting groups of __ and knowing how many groups have been counted)

• Square numbers (ex: 3 x 3)

• Nines (10 groups less one group, e.g., 9 x 3 is 10 groups of 3 minus one group of 3)

• Decomposing into known facts (6 x 7 is 6 x 6 plus one more group of 6)

• Turn-around facts (Commutative Property)

• Fact families (Ex: 6 x 4 = 24; 24 ÷ 6 = 4; 24 ÷ 4 = 6; 4 x 6 = 24)

• Missing factors

 

Refer to the 3.OA.7 Daily Discourse for opportunities to utilize these strategies

 

**Depending on the need of your students, developing this knowledge with concrete manipulatives (1- inch square tiles) and drawings might need to be utilized first.  Students can make arrays and explore the different ways to decompose and compose the arrays.  Then students can move to mentally solving these problems and fluently multiplying the groups of whole numbers.