Translating words to an expression

What it looks like when your child can do it

• — Your child writes "5 less than n" as n - 5 and can say why it is not 5 - n.
• — Given "n cookies shared equally by 3 children," your child writes n/3 and reads it back as the cookies each child gets.
• — Your child says the letter stands for the number of something, not the thing itself.

How to teach it at the kitchen table

1. 01

   Say what the letter stands for

   Before writing anything, finish this sentence out loud: let n be the number of... A letter is a number. Writing "n = apples" leads to reading 2n as two apples, which is wrong.

2. 02

   Match the words to the operation

   More than, plus and total usually mean add. Less than, fewer and left usually mean subtract. Times and each often mean multiply. Split, shared and per group mean divide.

3. 03

   Ask what was there first

   Order matters for subtracting and dividing. A jug holding 8 cups with j cups poured out is 8 - j. "Less than" flips the words: 5 less than n starts at n, so it is n - 5.

4. 04

   Put a whole group in parentheses

   When a whole group gets multiplied, wrap the group. Twice the sum of n and 5 is 2(n + 5), so the 2 doubles the n and the 5, not only the n.

5. 05

   Check with a number you know

   Put in a number and see if it matches the words. 5 less than 12 is 7, and n - 5 with n = 12 gives 7, so n - 5 is right.

You will need: Coins or buttons · A cup to hide some of them · Paper and a pencil

Try it together

1. Try 1

   Write "7 less than a number n."

   Listen for  n - 7. Writing 7 - n is the classic trap. Check with n = 10: 7 less than 10 is 3, and n - 7 gives 3, while 7 - n does not.

2. Try 2

   Tickets cost t dollars each. Write the cost of 4 tickets plus one 3 dollar parking fee.

   Listen for  4t + 3, where 4t means 4 times t. Only the tickets are multiplied by 4, since you pay for parking once. If your child writes 4(t + 3), ask how many times you pay for parking.

3. Try 3

   A pizza with p slices is shared equally among 3 people. Write the number of slices each person gets.

   Listen for  p/3, which is p divided by 3. The slices are what gets shared, so p goes on top. 3/p would mean 3 slices shared among p people.

4. Try 4

   Write "twice the sum of a number n and 5."

   Listen for  2(n + 5). The word sum makes n + 5 one group, and twice doubles the whole group. Check with n = 3: 2(3 + 5) = 16, while 2 x 3 + 5 = 11 doubles only the n.

Watch for

• — Writing "5 less than n" as 5 - n. "Less than" reverses the order of the words.
• — Writing d = dogs instead of d = the number of dogs.

If it is not there yet

• — Go back to phrases with numbers only, like "5 less than 12," and have your child write 12 - 5 before any letters come in.
• — Act it out with coins: hide some coins under a cup, set 3 more on the table, and write n + 3 for the total, where n is the number of coins under the cup.

A few days of this is normal, and it is time well spent. The lesson will still be there, and it will go faster.

Where this skill comes up

• Grade 6 Math Practice Workbook · Lesson 21

  A Letter for the Thing You Do Not Know

  Needs it because the situation has to become an expression before anything is solved.