A child can know that fourteen comes after thirteen and still find fourteen minus six difficult to picture. Use a small set of counters first, then a number line. Both models should show the same subtraction, with the six divided into four and two.
Give the six a visible meaning
Set out fourteen counters where the child can move them safely. For young children or households with younger siblings, use large suitable objects and put them away afterward. Ask the child to show the fourteen before taking anything away.
Explain the task as removing six from the fourteen. The six counts the objects removed; it is not the amount that remains. Separating those two meanings can prevent a correct piece of counting from answering the wrong question.
IES recommends well-chosen representations and number lines in elementary mathematics instruction. The calculations and activities here are original examples that apply those recommendations. Follow the school’s terminology if it differs. [1]
Remove four, then remove the remaining two
Move four counters into a separate group. Ten remain in the original group. Keep the removed counters visible so that the child can see they have removed four of the required six, not completed the whole subtraction.
Next move two more counters into the removed group. The removed group now contains six, and eight remain. Count both groups if needed. The original fourteen have been separated into six removed and eight remaining.
Record 14 − 4 = 10, followed by 10 − 2 = 8. Underneath, write 14 − 6 = 8. Ask why the second subtraction was two rather than another six. The explanation should refer to the four already removed.
Draw the same action as backward jumps
Draw an evenly spaced number line from zero to at least fourteen, and mark the numbers. Put a counter on fourteen. Move four intervals backward to ten, then two intervals backward to eight. Label the jumps minus four and minus two.
Count intervals crossed, not the starting tick. The first backward move from fourteen reaches thirteen. If the child counts fourteen as the first step, demonstrate one move and name the new position before continuing.
Compare the two models. The four counters in the first removed group correspond to the first backward jump; the next two correspond to the second jump. Ten is the intermediate stop, while eight is the result after removing all six.
Use an addition check without changing the original question
Put the six removed counters beside the eight remaining counters. Together they still make fourteen. Record 8 + 6 = 14 as a check, then point back to 14 − 6 = 8 so the child can explain how the two equations describe the same quantities.
Counting up from six to fourteen is another possible method, but you do not need to introduce every strategy at once. Stay with one coherent representation until the child can say what the numbers mean. More methods are not helpful if their purposes are becoming mixed together.
For a nearby example, try 13 − 5. Remove three to reach ten, then two more to reach eight. Ask the child to choose the first jump and explain why the second is two. If the explanation is uncertain, rebuild the quantities with objects rather than marking the attempt as careless.
References
Sources for the cited guidance and reported material. Worked examples and practical tools are original to Zolls.
- Institute of Education Sciences. Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades.