Understand and Represent Mixed Numbers

Students understand that a mixed number has a whole number part and a fractional part. They convert between mixed numbers and improper fractions using models and number lines, building the foundation for operations.

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Grade 4 · Adding and Subtracting Mixed Numbers · question 1 of 3

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20 rungs. A star at the top.

14/3 = 2/3

How it is taught

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A mixed number is wholes plus a leftover fraction.

An improper fraction can name that same amount.

Read it: One amount, two names

1 1/8 is 1 whole bar and 1 piece of another. The whole bar is 8 pieces of 1/8, so the same amount is 9 pieces: 9/8.

Count the pieces in each whole bar: 8 pieces of 1/8.
Count on through the pieces left over: 8, then 9.
Write the count over the same bottom number: 1 1/8 = 9/8.

8/8 is 1 whole, so a whole bar and 8 pieces of 1/8 shade the same amount.

Neither name is bigger: 1 1/8 and 9/8 shade the same bars.

To go back, make a whole bar from every 8 pieces: 23/8 is 2 whole bars and 7 pieces, which is 2 7/8.

A whole bar is as many pieces as the bottom number: count the wholes as pieces, then add the pieces left over.

Thinking 9/8 must be more than 1 1/8 because 9 is a bigger number.

Both name the same bars: 8 of the 9 pieces fill 1 whole bar, and 1 piece is left over.

6/4 = ___ — 1 2/4. Every 4 pieces make a whole, so 6/4 holds 1 whole with 2 pieces left: 1 2/4.

2 3/4 = 11/4

Imagine we baked some pans of brownies. We have two whole pans and a little bit of a third pan. How can we name that amount?

Here are two full pans. Each pan is one whole.

And our third pan is split into four equal pieces. Three of them are filled — that's three-fourths.

Together we write this as two and three-fourths. That's a mixed number — a whole number plus a fraction.

Now let's count in fourths. Each whole pan is four-fourths.

Grade 4 · A mixed number has a whole part and a fraction part

Four-fourths, plus four-fourths, plus three more fourths makes eleven fourths.

We can write that as eleven over four. This is called an improper fraction — the top is bigger than the bottom.

Let's check on a number line from zero to three, with each whole split into four fourths.

Two and three-fourths lands right here — two whole jumps, then three more little fourths.

And eleven fourths means eleven small jumps of one-fourth — landing on the very same spot.

So two and three-fourths and eleven-fourths are the same number, written two ways. Great job!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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