# MathBait™ Multiplication

# Fives

Share this resource!

A perfect introduction to prime factoring, students explore strategies for multi-digit products with a factor of 5 and find easier ways to compute. But not everything works out nicely! Some numbers seem to cause problems. . . help your students to problem-solve and determine why.

## Details

Resource Type

Activity

Primary Topic

Primes & Factoring

Unit

7

Activity

12

of

22

In this activity, we will reinforce the ideas developed in *Ninety*Â to help students easily determine the factor pair with values outside the multiplication table.

Begin by asking students the value of 8Ã—5. If students have completed the previous units in MathBaitâ„¢ Multiplication, they will be able to identify the product of 40. Explain this product is within our multiplication table so we are familiar with it, when values are outside the table they can be more tricky. We are going to learn how to make the tricky problems easier by forcing them back into our table.

Tell students to suppose they did not know what 8Ã—5 was, but they are really good at counting by tens and so they know 8Ã—10=80. Ask how they might use the fact 8Ã—10=80 to find 8Ã—5. Allow students to share their thoughts and ideas. Highlight the previous activity, as 8Ã—10=8Ã—2Ã—5. How might we use this fact to help us find 8Ã—5?

There are in fact multiple ways to go about this!

##### Method 1: Halving

Students are not yet familiar with division, so this is a fun way to get us thinking about halves. Since 8Ã—2Ã—5=80 we know 16Ã—5=80 as well. But our goal here was to find 8Ã—5. Looking closely, we can see 8Ã—5 is hidden in our expression 8Ã—2Ã—5=80. This tells us 8Ã—10 is double (or two times) 8Ã—5. Ask students how we could split 80 into two equal groups. In other words, what number could we add to itself to find 8? Students should be able to determine 4+4=8 and thus 4 tens + 4 tens = 8 tens or alternatively 40+40=80. If students are not flexible enough with addition, this might be challenging.Â

##### Method 2: Building 40

If your students are not yet ready to consider halving, stick to the methods shown in the activity *Ninety*. An alternative method to determine 8Ã—5 is to break up the 8. There are many ways to achieve this. Encourage students to find and share different methods. One way is to write 8 as 2Ã—4, which makes 8Ã—5=2Ã—4Ã—5. For here, students can notice this expression is equivalent to 10Ã—4 or to 2Ã—20, both easier facts to find. This is a good opportunity to get them thinking about halving by noticing 4 is half of 8, or two fours make 8. This view is further helping students in factoring as they are now thinking about how to break a number into 2 times something.

For the remainder of the activity, have students work independently or in pairs on additional problems.

12Ã—5

13Ã—5

14Ã—5

15Ã—5

16Ã—5

17Ã—5

Every problem except 13 and 17 can be broken down into a known fact. Here are some possible solutions:

12Ã—5=2Ã—6Ã—5=2Ã—30=60

12Ã—5=3Ã—4Ã—5=3Ã—20=60

14Ã—5=7Ã—2Ã—5=7Ã—10=70

15Ã—5=3Ã—5Ã—5=3Ã—25=75 (this is particularly good for students with a solid understanding of money)

16Ã—5=2Ã—8Ã—5=2Ã—40=80

16Ã—5=8Ã—2Ã—5=8Ã—10=80

Students will likely have a hard time with 13 and 17. In the next activities we will re-introduce prime numbers so this is a great time to discuss why these values are so hard to find! We introduced prime numbers in MathBaitâ„¢ Multiplication Part 2. Remind students as needed that a prime number is a tower height that can only be built with blocks which are 1-unit tall or, if we have a large block, can be built with one large block equal to the number. The values 13 and 17 are *prime*. We can only write them as 1Ã—13 or 1Ã—17, making our strategy not very effective.

Ask students if we can think of another way to determine 13Ã—5 or 17Ã—5, or any tricky value when dealing with a prime number. One way which we have explored previously in MathBaitâ„¢ Multiplication is using the distributive property. We can find,

13Ã—5 = (10+3)Ã—5 = (10Ã—5)+(3Ã—5) = 50+15=65.

Another method, not previous discussed, is to use the common theme of manipulation. We previously found 12Ã—5=60. We have learned this simply means we counted by 5's twelve times. Thus, thirteen times is simply one more 5, and so 13Ã—5=60+5=65. Encourage students to "try on" both methods of working with tricky primes to find 17Ã—5 and discuss what they liked and disliked about the process.

The material on this page is copyrighted by MathBait™. Please use and enjoy it! MathBait™ provides a temporary license for Non-Commercial purposes. You are not permitted to copy, distribute, sell, or make derivative work without written permission from MathBait™.

# Tell us what you think!

Click to rate this activity