Additional Materials
Materials Required
Estimated Time Needed
(Times are approximate and will depend on the needs of the students.)
The first activity is designed to help students interpret symbols and realize that the way the symbols are written defines the order of operations.
Note that one of the algebraic expressions on the slide does not have a match in words. This is deliberate! It is to help you explain the task to students.
Students may not be used to "talking algebra" and may not know how to say what is written or may do so in ways that create ambiguities.
For example, the following conversation between a teacher and pupil is fairly typical:
Teacher: Tell me in words what this one says.
[Teacher writes 3 + n⁄2 ]
Pupil: Three add n divided by two.
Teacher: How would you read this one then?
[Teacher writes:]
Pupil: Three add n divided by two. Oh, but in the second one, you are dividing it all by two.
Teacher: So can you try reading the first one again, so it sounds different from the second one?
Pupil: Three add... [pause] ...n divided by two [said quickly]. Or n divided by two, then add three.
Some students may notice that some expressions are equivalent; for example 2(n + 3) and 2n + 6. You do not need to comment on this now: when the Card Set C: Tables is given out, students will notice this for themselves.
Card Set C: Tables will make students substitute numbers into the expressions and will alert them to the fact that different expressions are equivalent.
There are shortcuts that will help to minimize the work. For example, some may notice that:
Allow students time to discover this for themselves. As they do so, encourage them to test that they match for all n.
This is the beginning of a generalization.
This last question is an important one and will be followed up in the next part of the lesson.
These envelopes can be reissued in the next lesson.
The Card Set D: Areas will help students to understand why the different expressions match the same tables of numbers.
These posters will be displayed in the final class discussion.
For example E1 is equivalent to E10, E8 is equivalent to E9, and E4 is equivalent to E5.