Download Print Version
Font:

Factors and Multiples

Strand: Number
Outcome: 3

Step 4: Assess Student Learning

Guiding Questions

• Look back at what you determined as acceptable evidence in Step 2.
• What are the most appropriate methods and activities for assessing student learning?
• How will I align my assessment strategies with my teaching strategies?

Sample Assessment Tasks

In addition to ongoing assessment throughout the lessons, consider the following sample activities to evaluate students' learning at key milestones. Suggestions are given for assessing all students as a class or in groups, individual students in need of further evaluation, and individual or groups of students in a variety of contexts.

A. Whole Class/Group Assessment

Examples of Whole Class/Group Assessment  

B. One-on-one Assessment

For students having difficulty with factors and multiples of numbers, as well as prime and composite numbers, begin with smaller numbers in a problem-solving context that is of interest to students. Provide manipulatives to use and guide students by asking questions that build on their previous knowledge and stimulate thinking and discussion. Guiding questions may be needed to help students understand the relationships between factors and multiples of numbers and how they connect to prime and composite numbers. Reinforce the meaning of the terms as necessary.

Guide students through the series of activities described below, providing clarification where needed. For example, you may have to create the first rectangle for the student. Then ask how many rows there are and how many tiles are in each row. This focuses attention on the factors of 12 and also on labelling the length and width of the rectangle that is drawn on grid paper.

When the student sorts the numbers into two groups in part f (see below), it may be necessary to use the tiles to represent each number and make the necessary arrays. As the student develops understanding, encourage efficiency by asking the student if he or she can list the factors without using the tiles; i.e., by dividing a number into the given number to see if it divides evenly without a remainder. In doing so, the student is reinforcing understanding of number facts.
 
Sample Problem

Make a rectangular dog pen using 12 square tiles. Each square tile is one square metre.

1. Use the tiles to make all the possible dog pens.
2. Draw and label a diagram of each rectangle on the centimetre grid paper. Pick the dog pen that you think a dog would like the best. Why do you think so?
3. Write a list of the numbers used for the length and width of the pens. How many are there?  These numbers are called factors of 12 because they divide evenly into 12.
4. Find all the factors of 18 by using 18 square tiles to make all the possible rectangles. How many factors are there?
5. Find all the factors of 11 by using 11 square tiles to make all the possible rectangles. How many factors are there?
6. Sort the numbers 2, 3, 4, 5, 6, 7, 8 into two groups: those that have exactly two factors and those that have more than two factors.
7. Numbers with exactly two factors are called prime numbers. Numbers with more than two factors are called composite numbers. Give another example of each. Explain.
8. What about the number 1? How many factors does it have? Is it a prime number? Why or why not? Is it a composite number? Why or why not?

To develop a deeper understanding of the concepts, see the activities using square tiles and arrays listed in Step 3, Section C: Choosing Learning Activities, such as:

• Sample Activity 1: Arrays and Area of Rectangles
• Sample Activity 1: Prime and Composite Numbers—Arrays and Graphing .

C. Applied Learning

Provide opportunities for students to use strategies for multiples, factors, primes and composites in a practical situation and notice whether or not these strategies transfer. For example, ask the student to solve the following problem and explain the thinking for solving this problem.
 
You jog every fourth day and swim every sixth day. On what days do you jog and swim? 

Does the student:

• use skip counting to find the multiples of 4 and 6?
• understand that the common multiples of 4 and 6 are 12, 24, 36, 48 … because both 4 and 6 divide evenly into each of these numbers?
• multiply 4 by 6 to get 24 but miss the answer of 12?
• apply multiples to other real-world problems? For example, Jimmy works every third day and Susie works every fifth day. On what days do they work together?