Lesson 3

Handy Facts

Est. Class Sessions: 2

Developing the Lesson

Part 1. Using Constant Hoppers to Multiply

Ask students to use the first three number lines on the Handy Constant Hopper page in the Student Activity Book to show how a +3, +2, and +1 constant hopper hops ten times. Point out to students that they are to write only the numbers at the points where the hopper lands. Figure 1 shows three completed number lines.

After students have had time to complete Questions A–C, ask one volunteer to show how a +3 hopper hops ten times on a display of the page. Ask another volunteer to show the hops on the class number line. As the student points to the hops on the number line, ask the class to skip count aloud by 3s. Ask one of the volunteers to write a multiplication number sentence to match the hopper's moves.

Then, ask the class:

X
  • Do you agree with this number sentence? Tell me what the numbers in the multiplication number sentence stand for. (Yes, I agree that 10 × 3 = 30 because the 10 shows the number of hops and the 3 shows how far it hopped each time. It stopped at 30.)
  • What if the +3 hopper only hopped 7 times? What is the multiplication number sentence? What do the numbers in the sentence stand for? (It would only go to 21. The number sentence is 7 × 3 = 21. The 7 tells the number of hops and the 3 tells how big the hops are. It stops at 21.)
  • What if the hopper stopped on 27? What is the multiplication number sentence? What do the numbers represent? (9 × 3 = 27. The 9 tells the number of hops and the 3 tells the size of each hop. The 27 is where it stops.)
X

Factors. In a multiplication problem, the numbers that are multiplied together are called factors. In the problem 3 × 4 = 12, 3 and 4 are the factors. Factors are whole numbers that can be multiplied together to get a number. For example 1, 2, 3, 4, 6, and 12 are all the factors of 12.

Product. The answer to a multiplication problem is the product. For example, in the problem 3 × 4 = 12, the product is 12.

Multiples. A number is a multiple of another number if it is evenly divisible by that number. For example, 12 is a multiple of 2 since 2 divides 12 evenly. When we skip count by 2s, we call out the multiples of 2: 2, 4, 6, 8, 10, etc.

Review the terms factor and product. Students were introduced to the terms in Unit 3 Lesson 3 Multiplication Stories and Lesson 4 Making Teams. Remind students that when multiplying, the two numbers multiplied together are factors and the answer is called the product. Ask them to identify the factors and the product in the number sentences they discussed for the constant hopper.

Repeat the discussion for the +2 and +1 constant hoppers with one volunteer using the class number line and the other using the display.

Assign Question D. Begin a discussion of the 0 constant hopper by asking students to discuss with a partner what the number line will look like when a 0 constant hopper hops 10 times. Ask them to write a number sentence that matches. Figure 2 shows an interpretation of a 0 constant hopper hopping ten times and a number sentence.

Ask volunteers to explain their thinking to the class and see if the class agrees.

Ask:

X
  • How far does the 0 constant hopper move on each hop? (It can't move off zero because a zero hop doesn't go anywhere.)
  • How far does the 0 constant hopper move on ten hops? (No matter how many times it hops it will still land back on zero.)
  • What is a number sentence that matches? (10 × 0 = 0)
  • What is a number sentence that shows how far it would go on 100 hops? (100 × 0 = 0)
Student Guide:
Student Activity Book: 259 260
Answers
X
SG_Mini
+
X
SG_Mini
+
Master:
+3, +2, and +1 constant hoppers hopping ten times
X
+
An interpretation of a 0 constant hopper hopping ten times
X
+