Decimal grid (hundredths)

What the grid shows

A decimal grid is one whole split into 100 equal squares. Each square is one hundredth (0.01), and each column of 10 squares is one tenth (0.1). Tap squares or drag across them to shade, or use the buttons to add or remove a tenth or a hundredth at a time. The readout shows the shaded amount as a decimal, as a fraction out of 100 and in simplest form, and as a percent, and it breaks the number into tenths and hundredths.

Why one picture helps

Decimals, fractions and percents are three ways of writing the same amount, but children often meet them in separate lessons and never connect them. On a hundred grid, 35 shaded squares are plainly 35 hundredths, so 0.35, 35/100, 7/20 and 35% are not four facts to memorize but four names for one picture. The grid also makes place value concrete: a column is worth ten single squares, which is exactly why the tenths digit is worth ten times as much as the hundredths digit.

Common mix-ups

• Thinking longer decimals are bigger. 0.35 looks bigger than 0.4, but shading both shows 0.4 is 40 squares and 0.35 is only 35.
• Reading 0.05 as 0.5. Five squares is a small corner of the grid; five columns is half of it.
• Treating percent as a different kind of number. Percent means per hundred, so 35% is 35 squares out of 100, the same as 0.35.
• Simplifying 35/100 by dividing only one number. Divide the numerator and denominator by the same number: both divide by 5, so 35/100 = 7/20.

A 10-minute activity

• Minutes 1 to 2: shade one column and ask how many squares it has and what part of the whole it is.
• Minutes 3 to 5: shade 0.35, then start again and shade 0.4. Ask which is greater and let the grid settle it.
• Minutes 6 to 8: shade 25, 50 and 75 squares and record the decimal, simplified fraction and percent in a three-column table.
• Minutes 9 to 10: press Challenge two or three times. Until the goal is reached, the readout only counts squares, so the child does the converting.

Where it fits by grade

• Grade 4: writing tenths as hundredths, such as 3/10 = 30/100 (Common Core 4.NF.C.5), using decimal notation for fractions with denominators 10 or 100 (4.NF.C.6), and comparing decimals to hundredths (4.NF.C.7).
• Grade 5: reading, writing and comparing decimals, and adding and subtracting decimals to hundredths.
• Grade 6: a percent of a quantity as a rate per 100 (6.RP.A.3c).
• England: Year 4 pupils recognize and write decimal equivalents of any number of tenths or hundredths, and Year 5 pupils learn that percent means parts per hundred and write percentages as fractions with denominator 100 and as decimals.

Learning more

Decimals, fractions and percentages each have their own skills on Eurekami's skill map, and lessons move between them using pictures like this grid. Daily Practice mixes the three together in short reviews, which is where many children finally see they are the same idea.