Increasing Patterns

Strand: Patterns and Relations
Outcome: 2

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 Word Document

B. One-on-One Assessment

Give the student some samples of pictorial increasing and repeating patterns that are on strips of paper and have been shuffled. Ask the student to sort these into patterns that are repeating or increasing. Can the student sort these accurately?

If not, move back to the concept of pattern and ask the student to identify patterns in various settings from a Unifix train that is made up of cubes in random order with ones that have two colours in a repeating pattern to numbers in random order to numbers in a patterned sequence such as 2, 4, 6, 8. If the student recognizes pattern, move on to repeating patterns and check to see if the student can identify the core of repeating patterns in which the core may vary up to five elements.

If the student sorted the repeating and increasing patterns accurately, take the cards away and ask the student to build with any of the manipulatives you have on hand a repeating pattern (tiles, pennies or bingo chips, and pattern blocks). If the student constructs a repeating pattern, consider how basic it is, such as ababab. Ask the student to build one more with a different pattern. Can the student build a different pattern? Can the student build one with more than two elements, such as abcabcabc? If not, begin work on repeating patterns to increase the complexity of the repeating patterns in the student's repertoire.

If the student seems to have a reasonable grasp of repeating patterns, you want to find out what grasp of increasing patterns the student has. Ask the student to build with any of the manipulatives an increasing pattern. Observe whether the student builds a pattern that is arithmetic or geometric. With manipulatives, the student often builds a pattern that is geometric or grows by a pattern, but when moving to numerals, often builds patterns based upon the addition of a constant (arithmetic). If the student cannot build one increasing pattern, you need to start working to move the student from recognition that a pattern is not repeating but increasing in a predictable pattern, to being able to figure out how it is growing and extend such a pattern.
If the student built a geometric increasing pattern, ask for a second and/or third to be sure that he or she does not just have one or two memorized. If they were all geometric, ask the student to show you a pattern on the hundred chart or with numerals. This one is more likely to be an arithmetic increasing pattern, such as counting by fives. If the student shows you one, ask him or her how it is growing. Then ask for several other increasing or growing patterns with numbers. Ask for an explanation of how each is increasing. If the student cannot show one on the hundred chart or with numerals, then you know that the difficulty lies within the transfer of increasing patterns to numerals or confusion exists because there are two types of increasing patterns. In the case of the latter, start building on the work to show students that both of these patterns are increasing, one by a constant and one by increasing amounts that unfold in a pattern. In the case of the former, start with manipulative and pictorial representations of patterns and connect them to their numeric representation.

C. Applied Learning

Have the students identify patterns in the environment and discuss whether they are repeating or increasing patterns. Ask for parents' assistance in doing so in the students' everyday experiences and encourage them to prepare their children to share these examples with the class.
Have the students do problems that entail using increasing patterns and point out to the students that they solved these problems by finding the increasing pattern and extending it. For example, involve the class in figuring out how much time it will take for everyone to share their work, if they are each given 2 minutes to share and it takes 1 minute between student sharing for the student to sit down and the next one to come up to the front. Encourage parents to involve their children in problems involving patterns. Warn parents that the students generally are not working with numbers larger than one hundred. For example, if mom and dad agree to spend $20 on each person's Christmas stocking and there are five people in the family, how much money will they spend on the stockings?
Have the students organize with patterns in their environment. Ask the students how we can organize our class library so it will be easier to find books on topics that you like or easier to know if all the books have been returned?
Have the students organize their data from science experiments in class to examine for patterns.
Have the students do some experiments and look at data for growing patterns in situations where the actual experiment would not be a good use of time, is not wise or is not possible. For example, if a toy car accelerates down a ramp of a particular length and angle in a certain number of seconds, and the same car travels down two other ramps that are 15 centimetres longer but raised the same amount as the first and the acceleration times are recorded. Is there a pattern in the time taken that will allow you to predict the time it would take for the car to travel down a ramp longer than you have? If you wanted to know how high a basketball would bounce if it were dropped off the roof, could you figure it out without climbing on the roof? If it is dropped from 1 metre, how high does it bounce? If it is dropped from 2 metres, how high did it bounce? Does someone know how high the roof is?

Related Resources

Assessment in the Mathematics