A B C D

Notes for Session 10, Grades K-2, Part C

Note 6

It is often difficult for teachers to see how the mathematics content at their grade level builds algebraic thinking. Therefore, it is important to look at many examples of elementary mathematics that build bridges to algebraic thinking.

Groups: Work on the problems from Groundworks, recording answers to questions (a)-(f) as you do each problem. In Problem C1, the goal is for students to predict and verify the numbers of characters in a pattern. Some questions to ask, as suggested by the authors, include:

 • What is the pattern? • How many Xs are in the pattern? • How many Os are in the pattern? • What will you draw in the first box? Second box? Third box? Fourth box? Fifth box?

You may think that your students will have difficulty predicting the character in each box without filling in the entire strip. Students should be encouraged to find ways of predicting without having to do the filling first.

In Problem C2, the goal is to recognize that a balance scale in essence represents equality. Some questions the authors suggest are:

 • What does Scale B show? • In Scale A, what blocks are in the left pan? In the right pan? • In Scale A, which pan is heavier?

In Problem C3 and C4, the goal is to figure out the function rule from the example, and then to apply the rule to determine the output when given the input, and the input when given the output. Students are also asked to find a rule that describes what the machine does.

Some questions the authors suggest include:

 • What shape went into the first machine? • What shape came out of the first machine? • What shape went into the second machine? • What shape came out of the second machine? • What is alike about the two figures that came out?

In Problem C5-C7, the goals are the same as Problem C3. Some questions suggested by the authors are:

 • Look at the first example. What number goes in? What number comes out? • Look at the second example. What number goes in? What number comes out? • What do you think the machine is doing?

Students may find it useful to act out what is happening in these machines.

In Problem C8 and C9, the goal is to apply the function rules to determine the output when given the input, the input when given the output, and also to describe the rule.

Questions to ask, as suggested by the authors, include:

 • What number goes into the stepper first? • What does the first part of the stepper do to the number? • What does the second part of the stepper do to that number? • What is the final result?

 Session 10, Grades K-2: Index | Notes | Solutions | Video