Same fraction. New groupings.

SparkClass

Break the colored part into groups, write the sum, then join every piece back together.

CCSS 4.NF.B.3b
One Bar · One Whole
Total Conserved
3/4 colored4 Equal Unit Pieces

Each group has one unit piece. Choose fewer groups to drag a boundary.

Joined · No Space Added
01

Three groups, one total. The groups contain 1 + 1 + 1 = 3 unit pieces, so the colored amount is still 3/4.

Colored Total3/4
Groups3
Whole1

Make the sum visible

Start with the unit pieces, then move to notation. Every equation on this page describes parts of the same one whole.

1

Count before grouping

Use 3/4. Ask: What does each one-fourth piece represent? How many are colored? Confirm that all four pieces together make the same whole.

2

Record more than one decomposition

Compare 1/4 + 1/4 + 1/4 with 2/4 + 1/4. Change the group count and drag boundaries. After each move, ask students to explain why the numerators still sum to 3.

3

Name a group without changing it

In the 2/4 + 1/4 preset, turn on simpler names. The two one-fourth pieces can be named 1/2, giving 1/2 + 1/4. This is only a new name for that group; no pieces are added, removed, or resized.

4

Separate, then justify the total

Separate the groups and use the manual slider to pause partway. The spaces appear inside the original whole, and the colored widths are unchanged. Join the groups to restore the original contiguous model.

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Listen for this misconception

If a student adds denominators, return to the unit-piece check: “How many one-fourths are colored altogether?” The denominator names the piece size; it is not a count of pieces to add.

CCSS 4.NF.B.3b: Decompose a fraction into a sum of fractions with the same denominator in more than one way, record each decomposition by an equation, and justify decompositions with a visual fraction model. Examples include 3/8 = 1/8 + 1/8 + 1/8 and 3/8 = 1/8 + 2/8. Optional simpler names (for example, calling a 2/4 group 1/2) rename a group without changing its pieces. The interactive model uses proper fractions only.