For a parent or an older brother or sister

Where the invisible plus sign hides

Grade 6 · Mathematics · Term 1, Week 7

This week your child multiplies fractions with whole numbers and with mixed numbers like 2½. Almost every mistake at this stage comes from one place: reading 2½ as “two times a half”. It means two and a half. The plus sign is invisible but it is there, and ten minutes of cutting fruit or paper makes it impossible to forget.

The activity — ten minutes, one sitting

What you need: five things that can be halved — bananas, pandesal, sheets of paper, bottle caps drawn on and cut — and a pencil.
  1. Put out two whole items and one half. Ask “How much is here?” Two and a half.
  2. Say “Write that as a number.” They write 2½. Then ask “Read it aloud to me.” Listen for the word and. If they say “two times a half”, point back at the table.
  3. Now cut the two whole ones in half as well. Count the halves out loud together: one, two, three, four — and the one already there makes five. Five halves. That is what 2½ is, and it is why the 2 becomes 5 and not 3.
  4. Say “Now I want half of all of it.” Slide half the pieces aside. Count what is left: two and a half halves — one and a quarter.
  5. Ask the question that matters: “We multiplied by a half. Did it get bigger or smaller?”

Three things to avoid

  1. Do not let “two and a half” be read as two times a half. Every time it happens, ask them to read it aloud rather than correcting it yourself.
  2. Do not say a whole-number answer must be wrong. Sometimes fractions multiply to a whole number, and it is a correct answer, not a slip.
  3. Do not insist they tidy the fraction straight away. Leaving it as 20/6 until the very end is easier and loses nothing; simplifying is taught later in the week.

How to tell it is working

  1. They say and when they read a mixed number, without thinking about it.
  2. Converting 3⅓, they count thirds rather than reaching for a rule.
  3. They predict whether an answer will be bigger or smaller before working it out.
If they are stuck, drop the mixed numbers entirely and do halves of whole things — half of four bananas, half of six. Come back to 2½ only when “two and a half” is being said out loud every time.