Texas Math Models

Try “number line” or “4.5D”

TEKS 4.2G · Grade 4

Decimals and fractions that mean the same thing

Seeing that 0.7 and 7/10 and 70/100 are three names for one amount, using grids, strips and money.

The standard itself reads: “4.2G: relate decimals to fractions that name tenths and hundredths”

This one is free on Teachers Pay Teachers: the whole set, not a preview.

One of them, worked all the way through

The Student Exemplar page for question 2: A strip is cut into 10 equal parts and 3 are shaded. Write that as hundredths. The correct answer is marked, and the question is worked out underneath.
  1. Three parts out of ten is 3/10, which is 0.3.
  2. Cut each of those ten parts into ten again and there are a hundred parts. The same shading now covers 30 of them.
  3. So 3/10 is 30/100, and 0.3 is 0.30. The amount never changed; the pieces got smaller.

This is one way, not the only way. The printable shows the same question worked more than one way, because children get there differently.

What usually goes wrong, and what helps

Each of these is a different misunderstanding rather than a slip, so each one needs something different. Find the one that sounds like your kid.

The student reads a hundredths grid as tenths, so every digit lands one place too far left
Count the little squares in one column, then in the whole grid. Ten and a hundred are different wholes.
The student changes the bottom number of a fraction without changing the top one
If the pieces get ten times smaller, you need ten times as many of them. The top and bottom numbers move together.
The student names the part that is NOT shaded
Ask “which part is the question about?” before counting anything.
The student writes hundredths with three decimal places, which makes them thousandths
Two places after the point is hundredths. Three places is thousandths, which is a different size again.

Try this at home

Money is the easiest way in. A dime is a tenth of a dollar and a penny is a hundredth, so 43 cents is 0.43 and 43/100 without anyone having to be told.

where these methods come from The strategies behind it: the Decimals chart and the Fractions chart.

What’s in the printable

Four questions on this skill, two to a page. The rest of the file is for the adult: an answer key, a worked solution for every question, and teacher pages on what each wrong answer means. 10 pages in all.