FocusRecognizing and generating equivalent fractions with fraction tiles and number lines, including comparison of fractions with different denominators.
Materials & Prep
Fraction tiles, individual number lines from 0 to 1, pencils, recording sheet, display number line, prepared fraction cards showing halves, thirds, fourths, sixths, and eighths.
Opening and Diagnostic Comparison
7 minContentFraction size depends on the amount represented by each equal part, not on the denominator alone. On the same whole, 1/2 is greater than 1/3 because halves are larger parts than thirds. The fractions 1/2 and 2/4 represent the same value.
Student taskUse fraction tiles to compare 1/2 and 1/3, record the greater fraction, and explain the comparison with a drawing or labeled statement. Predict whether 1/2 and 2/4 have equal values.
EvidenceComparison recording showing correctly aligned tiles and a written or drawn justification that 1/2 > 1/3; prediction for 1/2 and 2/4.
Modeling Equivalent Fractions
10 minContentEquivalent fractions name the same amount. Partitioning each half into two equal parts produces four equal parts in the whole, so 1/2 = 2/4. Partitioning each third into two equal parts produces six equal parts, so 1/3 = 2/6. Multiplying both numerator and denominator by the same nonzero number creates an equivalent fraction, while the model must show the unchanged total amount.
Student taskBuild 1/2, 2/4, 1/3, and 2/6 with fraction tiles; record each pair as an equation; shade matching portions on a whole model.
EvidenceCompleted model and equations showing equal lengths or areas for both pairs and correct identification of the numerator and denominator changes.
Guided Practice with Fraction Tiles
12 minContentEquivalent fractions can be generated by subdividing each unit fraction into the same number of smaller parts. Examples include 2/3 = 4/6, 3/4 = 6/8, and 1/2 = 4/8. The numerator counts selected parts and the denominator counts all equal parts in the whole.
Student taskComplete fraction-card matches using tiles, generate one equivalent fraction for each of 2/3, 3/4, and 1/2, and represent each pair with aligned tiles and a labeled equation.
EvidenceMatched card set and recording sheet with three accurate equivalent-fraction equations supported by models.
Number-Line Representation and Independent Application (14 minutes)
ContentEquivalent fractions occupy the same point on a number line from 0 to 1. For example, 1/2, 2/4, and 4/8 all locate at the midpoint. Fractions with different denominators can be compared by locating them on the same whole number line, not by comparing denominator numerals. The fractions 1/3 and 1/2 locate at different points, with 1/2 farther from 0.
Student taskPartition number lines into halves, fourths, and eighths; mark and label 1/2, 2/4, and 4/8; then partition a second number line into thirds and sixths and mark 1/3 and 2/6. Generate an equivalent fraction for 2/3 and 3/4 and place both the original and generated fractions on number lines.
EvidenceAccurately partitioned number lines, coincident points for equivalent fractions, correct placement of 1/3 and 1/2, and two generated fractions placed at matching values.
Exit Assessment
7 minContentEquivalent fractions represent the same quantity through equal models, equal locations on a number line, or matching multiplication of numerator and denominator.
Student taskComplete three items: circle the fraction equivalent to 1/2 from 2/4, 2/3, and 3/8; draw a model or number line proving the answer; generate an equivalent fraction for 3/5 and explain why the numerator and denominator change together.
EvidenceIndividual exit response with one correct selection, one valid visual representation, one accurate generated fraction, and an explanation connecting equal value to the model.
Assessment criteriaProficient work identifies equivalent fractions as equal values, uses fraction tiles or number lines to prove equality, generates equivalent fractions by applying the same factor to numerator and denominator, and compares 1/3 and 1/2 according to the size of the parts rather than the denominator numeral.
DifferentiationA labeled fraction-tile and number-line reference sheet with a reduced problem set for students requiring support; additional generated equivalents and comparison of non-unit fractions for extension.