Multiplying Decimals Visually: Choco Decimals

Choco Decimals is a digital tool for multiplying decimals. Students can often count the decimal places and get the right digits, but ask them why 0.4 × 0.3 is smaller than both numbers, and the rule falls apart. They put the point in the wrong place, they turn 35 hundredths into 3.5, and they're surprised when "multiplying" makes a number smaller.

In Choco Decimals, every decimal is chocolate. One bar is 1 whole, a column is a tenth and a single piece is a hundredth. Students build the decimal first, then they do the multiplying themselves: they make the groups and pour them together, or shade across and down and put the overlap into one bar. The answer is something they can count.

Watch it in action

The tool runs in any web browser. There's nothing to print or set up, and students don't need logins.

Build the decimal first

Every problem starts with the decimal itself. For 0.35 × 3, students first build 0.35: they tap a piece, and the bar fills up to it, column by column. Counters under the bar show the columns and the pieces: 3 full columns and 5 pieces.

A chocolate bar of 100 pieces with 0.35 filled in: 3 full columns and 5 pieces

A student who builds 5 columns and 3 pieces is told they swapped them: 0.35 has 3 tenths (full columns) and 5 hundredths (single pieces).

A bar with 0.53 built for 0.35, and the hint: You swapped them

× a whole number: make the groups

× 3 means 3 groups of 0.35, and students make them. They tap + Add a group until there are 3 copies of their bar, each in its own flavor. Too many or too few, and the tool says how many groups they have and how many × 3 needs.

0.35 × 3: two groups of 0.35 made so far, with the + Add a group button

Pour them together

Then students tap each group to pour it into the answer bars. The pieces fill the bars after the ones already there, so when a bar is full, the next group spills into a new one.

Two groups poured into the answer bars, the third group still waiting

After the third group, there's 1 full bar and 5 more pieces: 1 whole and 5 hundredths. Students type the answer, 1.05.

0.35 × 3: one full bar in three flavors and 5 pieces in the next bar, with 1.05 typed in

With tenths, it's the same idea with full columns: 0.4 × 3 is 12 columns, a whole bar and 2 more columns, so 1.2.

0.4 × 3: one full bar and two columns, with 1.2 typed in

× a decimal: across and down

Times a decimal is the area model. For 0.4 × 0.3, students shade 0.4 across in blue (4 columns), then 0.3 down in yellow (3 rows). Where the two overlap is the answer, in chocolate.

The area model for 0.4 × 0.3: 4 columns across in blue, 3 rows down in yellow, the overlap in chocolate

Put them together moves the chocolate overlap into one bar, so it can be read as a decimal: 12 pieces, 0.12. It's smaller than both numbers, and students can see why: it's part of a part.

The 12 overlap pieces put together in one bar, with 0.4 × 0.3 = 0.12

Decimal × decimal

For 1.3 × 0.6, 1.3 across takes two bars: 1 whole bar and 3 more columns. 0.6 down is 6 rows on both bars.

The area model for 1.3 × 0.6 across two bars, with 13 columns in blue and 6 rows in yellow

The overlap is 13 × 6 = 78 pieces. Put together, they fill 7 columns and 8 pieces of one bar: 0.78.

The 78 overlap pieces put together in one bar, with 1.3 × 0.6 = 0.78

The wrapper

Every step is written on the wrapper beside the bars, so the model and the numbers meet: across 1.3 = 13 columns, down 0.6 = 6 rows, together 13 × 6 = 78 pieces.

The key and the wrapper: across 1.3 = 13 columns, down 0.6 = 6 rows, together 13 × 6 = 78 pieces

Hints for the mistakes students make

Students who type 105 for 0.35 × 3 are told that each piece is only a hundredth. Answers that are off by a place, like 10.5 or 0.105, get "Check the place value." And in the area model, a wrong answer points back to the chocolate: count the columns times the rows, and each piece is a hundredth.

Correct! over the answer bars for 0.35 × 3

How it works, for every level

The first time a level is opened, it starts with a worked example on the bars, with a short explanation. It's always one tap away with the How it works button.

How it works for decimal × decimal: the overlap on two bars and the pieces put together

Six levels

Build decimals: show tenths and hundredths on a bar, like 0.35
Tenths × whole: like 0.4 × 3
Hundredths × whole: like 0.35 × 3
Tenths × tenths: the area model on one bar, like 0.4 × 0.3
Decimal × decimal: the area model across two bars, like 1.3 × 0.6
Word problems: pick the expression, then solve it on the bars

Every level makes new problems each time.

Word problems

"A chocolate bar weighs 0.35 kg. Maya buys 3 bars. How much do they weigh?" Students pick the matching expression first.

A word problem with three expressions to choose from: 0.35 + 3, 0.35 × 3 and 3.5 × 3

Picking 0.35 + 3 gets "3 bars of 0.35 kg each: that's 3 groups of 0.35." The right one is then solved on the bars, from building 0.35 to pouring the groups.

The hint for 0.35 + 3: 3 bars of 0.35 kg each, that is 3 groups of 0.35

Choco Decimals works on phones too.

Choco Decimals on a phone screen

What students practise

Representing tenths and hundredths on a hundredths grid
Multiplying a decimal by a whole number as equal groups
Multiplying a decimal by a decimal with the area model
Reading the product from full bars, columns and pieces
Seeing why multiplying by a decimal less than 1 makes a number smaller
Choosing the right operation in word problems

Teaching tips

Model How it works on the class board before students try a level.
Ask before they multiply: "Will the answer be bigger or smaller than the decimal?"
Estimate first. 0.35 is about a third of a bar, so 0.35 × 3 should be a little over 1.
Link the pieces to the digits. 13 columns × 6 rows = 78 pieces, so 1.3 × 0.6 = 0.78.
Read the wrapper aloud at the end, so the model and the written method meet.

Standards

5.NBT.B.7: multiply decimals to hundredths using concrete models and drawings, and explain the reasoning
5.NBT.A.1 and 5.NBT.A.3: place value of tenths and hundredths
5.NF.B.5: multiplication as scaling
6.NS.B.3: fluency with decimal multiplication