Mar 2, 2023 | Red Deer

Ask your child what is half of 8? For sure they can answer that it’s 4. Then reverse your question: Half of what number is 4? Many kids are confused. So what is it in reverse question that important for the growth of a child’s mathematical thinking?

This blog is part of our Wholes & Parts series, and will explain why we need the Reverse Question format.


The Reverse Question

Many teachers in the early grades tend to neglect or shy away from “advanced” language forms. The Reverse Question format is particularly neglected.

  • “What’s your bear’s name?” is a straight question. “Whose name is Teddy?” is a reverse question.
  • A straight question: “How many eyes do 3 people have altogether?” The reverse question: “If you see 8 eyes, how many people are there?”

Generally, in a Straight Question, we are given “parts” and asked to determine the “whole”.

In the Reverse Question format, we are generally given the whole and some of the parts, and we are asked to find the remaining part or parts.

Most word problems require the use of reverse-thinking process. This is why so many students have trouble with word problems they do not have an experience-base that includes early and frequent encounters with questions that involve the reverse-thinking process.

Don’t be surprised if your high-school child cannot answer “half of what number is 4”. Even it is common to see an adult cannot solve “half of what number is 7 ¼ ?” (which is actually a simple word problem), but can answer a straight question “what is double of 7 ¼?”, which is essentially the same thing.

This is because their experience-base does not include exposure to reverse questions to any meaningful degree. As a result, these students have a formidable obstacle if they are to continue their mathematical education.

Continuous use of the Reverse Question is an integral part of the Mathnasium Program, introduced early as a tool for learning problem solving skills. For instance, besides asking a straight question “what is 7 plus 5?”, we also ask “7 plus what number is 12?”


Other Examples of Reverse Question

Some other examples of Reverse Question to find missing numbers:

• “What number plus 3 equals 10?...100?...51/2?”

• “7 plus what number is 12?...1,000?...0?”

• “10 minus what number is 6?...100?...0?”

• “What number take away 7 is 6?...100?...0?”

• “What number 4 times makes 20?...100?...10?”

• “5 times what number is 20?...100?...21/2?”

• “What number divided by 6 is 4?...10?...1/2?”

• “12 divided by what number is 3?...6?...1/2?”

When students are used to think reversely back and forth, they would be able to see the big pictures of the problems, can identify quickly which ones are wholes and which ones are parts as demonstrated by this 7-year-old second grader in this video.



So, interact and engage with your child more than just asking a straight math question to nurture their problem thinking skills!


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