How to find the math gaps holding your 7th grader back

Five skill areas to check, in order

1. Whole numbers: adding and subtracting with regrouping.
2. Multiplying and dividing: facts first, then larger numbers.
3. Fractions: equivalent fractions, then adding and subtracting with different denominators.
4. Ratios: equivalent ratios and rates.
5. Equations: solving for the unknown, one step then two.

Have your child try two questions from each area below, out loud, while you watch how they work. Don't help and don't hurry. What they do matters more than whether the answer is right.

Sample questions, with answers

Each question below was checked by two separate programs. The tempting answers are the ones a child gets by making a typical slip, so you can see what a slip looks like.

1. What is 239 + 677?

   • A. 816
   • B. 906
   • C. 916Answer
   • D. 806
   What the other answers come from

   • 816: Tens Carry Missed. When the tens add past nine, carry the extra hundred to the next column.
   • 906: Ones Carry Missed. When the ones add past nine, carry the extra ten to the next column.
   • 806: Columns Apart. Add one column at a time, and carry the extra over to the next column.

2. What is 693 + 138?

   • A. 831Answer
   • B. 821
   • C. 731
   • D. 721
   What the other answers come from

   • 821: Ones Carry Missed. When the ones add past nine, carry the extra ten to the next column.
   • 731: Tens Carry Missed. When the tens add past nine, carry the extra hundred to the next column.
   • 721: Columns Apart. Add one column at a time, and carry the extra over to the next column.

3. What is 79 × 7?

   • A. 553Answer
   • B. 493
   • C. 112
   • D. 499
   What the other answers come from

   • 493: Carry Left Behind. Add the regrouped tens to the next product.
   • 112: Place Value Slip. Tens are worth ten each. Write each part in its place before you add.
   • 499: Ones Left Alone. Multiply the ones digit too, then the tens digit.

4. What is 47 × 7?

   • A. 77
   • B. 287
   • C. 329Answer
   • D. 289
   What the other answers come from

   • 77: Place Value Slip. Tens are worth ten each. Write each part in its place before you add.
   • 287: Ones Left Alone. Multiply the ones digit too, then the tens digit.
   • 289: Carry Left Behind. Add the regrouped tens to the next product.

5. What is $\frac{3}{8} + \frac{5}{12}$?

   • A. $\frac{7}{12}$
   • B. $\frac{1}{3}$
   • C. $\frac{19}{24}$Answer
   • D. $\frac{2}{5}$
   What the other answers come from

   • $\frac{7}{12}$: Half Changed. Change both fractions to the new bottom before you add or subtract.
   • $\frac{1}{3}$: Top Left Behind. Changed the bottom? Change the top by the same amount.
   • $\frac{2}{5}$: Straight Across. Adding fractions? Make the bottoms match first.

6. What is $\frac{1}{3} + \frac{5}{7}$?

   • A. $1\frac{1}{21}$Answer
   • B. $\frac{2}{7}$
   • C. $\frac{4}{7}$
   • D. $\frac{3}{5}$
   What the other answers come from

   • $\frac{2}{7}$: Top Left Behind. Changed the bottom? Change the top by the same amount.
   • $\frac{4}{7}$: Half Changed. Change both fractions to the new bottom before you add or subtract.
   • $\frac{3}{5}$: Straight Across. Adding fractions? Make the bottoms match first.

7. A pancake batter uses 4 eggs for every 5 cups of milk. At this rate, how many cups of milk are needed for 20 eggs?

   • A. 30 cups
   • B. 100 cups
   • C. 25 cupsAnswer
   • D. 21 cups
   What the other answers come from

   • 30 cups: One Batch Too Many. Count how many times the first amount fits, and use exactly that many.
   • 100 cups: Skipped the Divide. Find the amount for one by dividing, then multiply for the new amount.
   • 21 cups: Adding Both Sides. Ratios grow by multiplying. Find what you multiply by, then use it on both.

8. A pancake batter uses 5 eggs for every 3 cups of milk. At this rate, how many cups of milk are needed for 25 eggs?

   • A. 15 cupsAnswer
   • B. 18 cups
   • C. 75 cups
   • D. 23 cups
   What the other answers come from

   • 18 cups: One Batch Too Many. Count how many times the first amount fits, and use exactly that many.
   • 75 cups: Skipped the Divide. Find the amount for one by dividing, then multiply for the new amount.
   • 23 cups: Adding Both Sides. Ratios grow by multiplying. Find what you multiply by, then use it on both.

9. Solve for $x$: $3x + 9 = 42$

   • A. $x = 33$
   • B. $x = 11$Answer
   • C. $x = 17$
   • D. $x = 5$
   What the other answers come from

   • $x = 33$: Half Done. After you undo the plus or minus, divide by the number next to x.
   • $x = 17$: Sign Slip. Undo with the opposite: take away what was added, add back what was taken.
   • $x = 5$: Divided One Part. Divide every term on a side by the number next to x, not just one.

10. Solve for $x$: $2x - 2 = 14$

    • A. $x = 16$
    • B. $x = 8$Answer
    • C. $x = 6$
    • D. $x = 9$
    What the other answers come from

    • $x = 16$: Half Done. After you undo the plus or minus, divide by the number next to x.
    • $x = 6$: Sign Slip. Undo with the opposite: take away what was added, add back what was taken.
    • $x = 9$: Divided One Part. Divide every term on a side by the number next to x, not just one.

What a gap looks like

• Adding in a column and forgetting to carry: the answer is off by exactly ten or a hundred.
• Adding fractions by adding the tops and the bottoms: 1/2 + 1/3 becomes 2/5.
• Solving the first step of an equation, then dropping the number being added or subtracted.
• Setting up a ratio upside down.

Fluency gap or concept gap?

A fluency gap is slow or error-prone recall of something the child understands, like multiplication facts. A concept gap is not knowing why a method works. The test is simple: ask your child to explain, or draw, what the problem is asking. If they can, but they slip on the arithmetic, it is fluency, and short daily practice fixes it. If they can't, they need the idea explained again with a picture before more practice.

What to do with what you find

Fix the earliest shaky area first. If you'd like a guided version that does this check for you and then gives 20 minutes a day on the first gap, that is what Bridgil's starting check is for. For the full plan, read what to do after a Level 1, and for what the test itself covers, the grade 7 test format.

Keep reading

• 7th grader scored Level 1 in math: what to do now
• NYS grade 7 math test: format, topics and calculator