Colorado Grade 3 Math

Different partitions, the same shaded length

Draw two strips of equal length. The first is divided into two equal parts with one shaded. The second is divided into four equal parts with two shaded. Do the shaded regions represent different amounts, or the same amount?

Align the strips at the same starting point. Both shaded regions end halfway along the whole strip. The first labels that amount 1/2; the second labels it 2/4. The two fourths cover the same length as one half, so 1/2 = 2/4.

Explain what changes when the partition changes

The second strip has more pieces, but each piece is smaller. A fourth is half the size of a half, so two fourths join to make one half. More shaded pieces do not necessarily mean a greater shaded amount. Ask the student to name the size of each piece as well as the number shaded.

On a number line, use the interval from 0 to 1 as the whole. Partition it into halves and mark 1/2. Then partition an equal 0-to-1 interval into fourths and mark 2/4. The points occupy the same position. This connects the strip model with fractions as numbers, rather than treating a fraction only as a picture label.

Investigate a tempting mistake

A child may say that 2/4 is larger because two shaded pieces are more than one. Compare the pieces directly. One shaded half can be split into two fourths without making the shaded amount longer. A different error is to divide a strip into unequal pieces and label each one a fourth. Fold or measure the partition to show why equal parts matter.

Also check that the strips represent equal wholes. If the second strip is twice as long, its two shaded fourths may be physically longer than one half of the first strip. The fraction names describe proportions of their own wholes; a physical-length comparison needs a shared whole.

Create and defend another equivalence

Shade two thirds of a new strip and divide each third into two equal pieces. Four sixths are now shaded, and the total shaded length has not changed. Explain 2/3 = 4/6 using the same reasoning. Students can point to the paired pieces before writing an equation.

Use the explanation to choose practice. A student who can name shaded fractions but cannot compare their amounts needs more equal-whole models. A student who can show equality can try placing the equivalent fractions on a number line and writing a sentence that explains their shared position.

Selected Colorado Grade 3 evidence outcomes

The Colorado mathematics directory links the 2020 Colorado Academic Standards, adopted in 2018. The linked grade-band document was corrected in December 2019. These activity labels summarize selected evidence outcomes; the codes below are the CCSS references displayed in Colorado’s document. Read the complete grade expectations, mathematical practices, and Colorado context alongside them.

Sources checked October 5, 2026. This selected activity is one entry point for instruction; it is not a complete curriculum checklist.

Connect the explanation with practice

Use the lesson, worksheet, and quiz directory to choose a related skill. The existing resource links remain available; use an activity’s directions to understand its timer, tools, question count, and scoring.

Grade 3 is within the CMAS mathematics testing range. Classroom learning and an independent practice score serve different purposes; a practice score does not establish an official state performance level. Read Colorado’s official CMAS overview.

Keep one example of the student’s reasoning with the practice result. Use the error analysis in the activity to choose a smaller model, a related question, or a new context for the next session.