Grade Five SCO: B7

GCO B: Students will demonstrate operation sense and apply operation principles and procedures in both numeric and algebraic situations

KSCO: By the end of grade 6, students will have achieved the outcomes for entry - grade 3 and will also be expected to explore algebraic situations informally.

SCO: By the end of grade 5, students will be expected to determine whether an open sentence is always, sometimes or never true.

Students will conclude if an open sentence is true sometimes, all of the time or never. Previously  students believed that an open sentence is true with only one right number filling its place. They need to realize that they cannot immediately figure out the type of sentence just by looking at it and that sometimes there is one solution and sometimes there is more than one solution. The objective is to get students to practice writing open sentences without necessarily solving them each time.

Related SCOs:

 
Prior learning
Concurrent learning
Subsequent learning. 


2-C5: represent patterns using their own notation and or symbolism

2-C6: solve simple open sentences involving addition and subtraction facts

3-C5: recognize the meaning of open sentences of the forms:

A x B = ?

A x ?= C

?X B = C
 

 4-C6: complete open sentences of the forms:

                    A x B = ?

                    A x ? =C

                    A/B= ?

                    A/?=C


 

5-C2: recognize and explain the patterns in dividing by 10, 100 and 1000 and/or in multiplying by 0.1, 0.01, and 0.001

5-C3: solve problems using patterns

 6-B9: estimate products and quotients involving whole numbers only, whole numbers and decimals, and decimals only

6-C1: solve problems involving patterns

Useful Resource:

Berkman, Robert, M. (1998). "Exploring Interplanetary Algebra to Understand Earthly Mathematics." Teaching Children Mathematics 5(2).

    This article takes a unique approach to teaching grade 5 students algebra in a very basic way, such as completing open sentences. By using aliens and outer space as a teaching tool, the teacher is able to achieve further understanding through a concrete example. Since in the hypothetical situation the aliens had a different number of fingers on their hands than we humans do, children got to see that there may be different solutions to problems. The aliens got a different answer because they went about it a different way, which shows children that sometimes there are different ways of solving the same problem. Also there was a portion showing that sometimes there is one answer for a problem and children learned how to generalize this. In the example, the teacher also got the children to make up their own problems for each other and they worked them out in small groups. The goal of this wasn't to teach children the formal way to do algebra but to see connections between problems and to broaden their thinking. All they are trying to do is represent the missing information.

by Abbey Langille, based on a page by Heather Anderson and Nancy Summers


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