How do you write down an answer when you don't know the number yet? You leave it a place to go.
Not started yet.
By the end of this lesson your student should be able to look at an expression like 2h + 3w, replace each letter with the number it stands for, and work out the value.
The bigger idea underneath is what a variable is for. It holds the place of a number that changes, or that nobody knows yet, so a rule can be written down before the number exists.
Don't open with the word variable. Open with the babysitting table and ask which column never changes and which one changes on every row.
Once the student says the hours change, ask how Tammy could write one rule for a night that hasn't happened yet. Let the letter be the answer to that question, not a definition handed over first.
🚨 The biggest trap is reading 2n with n = 6 as twenty-six. Two things written side by side in algebra mean multiply, so 2n is 2 times 6, which is 12. Say it out loud as '2 times n' until it sticks.
The second trap is forgetting the order of operations once the letters are gone. After replacing the letters in 2h + 3w, the problem is an ordinary math sentence again, and multiplication still comes before addition.
Some students also think a letter is a code for one fixed number, the way a = 1 and b = 2 in a puzzle. It isn't. The same n can be 6 on Friday and 3 on Saturday.
The book models 2n with cups and counters. Put two cups on the table and tell the student each cup is n. Drop six counters into each one, count them, and you have 2n when n is 6.
Then empty the cups and put three counters in each. Same two cups, same expression, a different number in the place. That is the whole idea of a variable, and it's worth doing with the real cups.
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Before You Start
The words this lesson uses. Tap a card to see what it means, then come back to them whenever a question uses one.
Part One
Questions about the story you just read. Pick your answer straight off, or press Find it in the story if you would rather hunt for the sentence first.
Part Two
The word cards are at the top of this page. Look back at them as often as you need, then answer.