Evaluating an expression

What it looks like when your child can do it

• — Asked for 3n + 2 when n = 5, your child writes 3 x 5 + 2, then 15 + 2, and says 17.
• — Given 6(b + 1) with b = 4, your child writes 6(4 + 1) and works the parentheses first to get 30.
• — Your child knows 4n means 4 times n, so with n = 3 it is 12, not 43.

How to teach it at the kitchen table

1. 01

   A letter holds a number's place

   In 3n + 2, the n stands for a number you have not been told yet. Once you are told n = 5, the 5 goes wherever the n was.

2. 02

   Rewrite before you work

   Copy the expression with the number in place of the letter: 3n + 2 becomes 3 x 5 + 2. Writing this line first stops most mistakes before they start.

3. 03

   A number beside a letter multiplies

   3n means 3 times n, so with n = 5 it is 15, not 35. A number right before parentheses multiplies too: 6(b + 1) means 6 times whatever is inside.

4. 04

   Work in the right order

   Parentheses first, then multiplying and dividing, then adding and subtracting. For 3 x 5 + 2, multiply to get 15, then add 2 to get 17.

5. 05

   Same number in every place

   If a letter shows up more than once, like n + n + n, the same number goes in each place. With n = 8 it is 8 + 8 + 8 = 24.

You will need: Paper and a pencil

Try it together

1. Try 1

   Find 4k + 3 when k = 8.

   Listen for  35. 4 x 8 = 32, then 32 + 3 = 35. Watch for 51, which comes from reading 4k as the two-digit number 48.

2. Try 2

   Find 2(a + 7) when a = 3.

   Listen for  20. Parentheses first: 3 + 7 = 10, then 2 x 10 = 20. If your child gets 13, they multiplied only the 3 and added the 7 afterward.

3. Try 3

   Find 20 - 3m when m = 4.

   Listen for  8. 3 x 4 = 12, then 20 - 12 = 8. If your child gets 68, they subtracted first: 20 - 3 = 17, then 17 x 4.

4. Try 4

   Put y = 2 into both 6(y + 3) and 6y + 3. Do they come out the same?

   Listen for  No. 6(2 + 3) = 6 x 5 = 30, and 6 x 2 + 3 = 15. One number that gives different answers shows the two expressions are not the same, which is the check the grade 6 book asks for.

5. Try 5

   Is n = 7 a solution of 6n = 42?

   Listen for  Yes. 6 x 7 = 42, and the right side is 42, so the two sides match. Your child should say both sides out loud before answering.

Watch for

• — Reading 3n with n = 5 as 35 instead of 3 x 5 = 15.

If it is not there yet

• — Go back to order of operations with plain numbers, like 2 + 3 x 4 = 14, until multiplying before adding is automatic.
• — Write the expression with an empty box where the letter goes, have your child write the number in the box, then work it out. Switch back to letters once that feels natural.

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 19

  Are These Two Expressions the Same?

  Needs it because the test for equivalence is substitution.

• Grade 6 Math Practice Workbook · Lesson 20

  What It Means to Be a Solution

  Needs it because checking a candidate value is an evaluation: the value goes in for the letter and the expression is worked out.