Students physically measure and count cups to find that 2 cups = 1 pint, 4 cups = 1 quart, and 16 cups = 1 gallon (Activity 1, Activity 2, measuring of melted ice). Students create a foldable that illustrates the relationships among cups, pints, quarts, half-gallons, and gallons and answer questions such as how many half-gallons are in one gallon. Students estimate and measure capacities, record actual capacities in cups or pints, and use those measures to compare sizes of containers (Activity 3 and Activity 4).

Students are prompted to say times in more than one way (for example, "half past three" and "three thirty"), which links fractional language (half, quarter) to minute-based time equivalents. The lesson also uses quarter-hour language (a quarter after, a quarter to) and asks students to convert those to specific clock times, so students practice matching fractional parts of an hour to equivalent minute representations.

Students divide shapes and objects into equal parts (halves, thirds, fourths, ninths) using geoboards, apple pieces, paper folding, and snacks, and they name those parts using fraction words (one-half, one-fourth, two-ninths). Students identify equal and unequal parts through guided questions and an online "Equal Parts" game. Students also read and produce fraction labels (for example, two-fourths or two-quarters) when describing grouped pieces.

Students cut out "Matching Fractions" cards and create pairs that show the same fractions, directly matching written fractions to visual area models. Multiple activities (Naming Fractions, Colorful Circles) have students color or identify shaded parts of circles or shapes and write the corresponding fractions, so students practice recognizing fractions as quantities of the same-sized region. Reading questions also ask students to compare a half and a fourth of a pizza, prompting reasoning about which fraction is larger based on size.

Students make and use fraction strips (or fold paper strips into halves, fourths, and eighths), align them, and answer questions such as "How many fourths equal one half?", showing visual equal-size relationships. Students use interactive fraction tools to shade and compare fractions (e.g., show 6/12, 1/12, 10/12) and play games that isolate same-denominator or same-numerator cases to practice recognizing equal amounts in special cases. The skills and activities prompt students to record comparisons with the symbols >, =, or < and to justify conclusions about when fractions represent the same or different amounts.

Students color and combine fraction-chart pieces and fraction strips to show multiple representations of the same amount (for example, coloring 1/2 and then finding 2/4, 3/6, 4/8, 5/10, 6/12 that equal the same half). Students use pizza, circle, and square interactives and matching activities to show that fractions with equal numerators and denominators make 1 and that some different-looking fractions represent the same size. The lesson's skills list explicitly includes "Explain equivalence of fractions in special cases" and "Recognize and generate simple equivalent fractions."

Students are guided to represent fractions on number lines (partitioning 0–1, marking 1/b and a/b) and to plot given fractions (e.g., 1/3, 2/6, 3/10). Activities ask students to match labeled points on number lines with fraction names and to complete a "More Fraction Matching" task that groups three cards showing the same fraction as a numeric fraction, a shaded diagram, and a number-line point. The worksheet explicitly asks "What do you notice about 4/8 and 5/10?" and records the observation that they are the same (both one-half of the line).

Students physically overlay fraction circles and place one half on top of another and write 1/2 = 2/4 on the board, showing same-size equivalence. Students color and identify equivalent entries on a laminated fraction chart (e.g., color 2/3 then find and color 4/6, 6/9, 8/12). Students draw and partition identical rectangles into 2, 4, and 8 parts and shade equivalent amounts (one half, two fourths, four eighths) and complete worksheets that fill in missing numbers for equivalent fractions.

Students write and interpret equivalent fractional forms in the Fractions and Time activity (e.g., 45 minutes is given as 9/12 and 3/4). Students record equivalent representations of money amounts in Fractions and Money (e.g., 25¢ shown as 1/4 or 25/100, 50¢ as 1/2 or 50/100, 75¢ as 3/4 or 75/100). Several activities require students to produce fractions that describe the same quantity (e.g., bead counts for Fraction Bracelets and fraction parts of animals that sum to totals).

Students place fractions on number lines (tasks to put a dot on 2/5, 3/9, and to show 3/5 on a line with 0 and 1). Students identify and generate equivalent fractions using a fraction chart (find how many are equal to 1/2 or 1/3) and by matching pairs such as 5/6 = 10/12. Students connect equivalent fractions shown in different representations using Fraction Dominoes and answer test items asking which images are equal to one-half or which image is equivalent to a given fraction.

Students use geoboards and grids to partition shapes into equal parts and label each part with unit fractions (Activity 1 and Activity 2). Students shade and write fractions such as 1/2, 1/4, 1/8, and 3/9 and are asked to state what the numerator and denominator represent. In Activity 3, students divide a 12 cm² rectangle into halves, thirds, and fourths in multiple ways and are explicitly asked to show that parts that differ in shape can take up the same area, with the text noting that "the parts don't have to be the same shape as long as they take up the same area."

Students use pattern blocks to cover and partition a hexagon with trapezoids, rhombuses, and triangles (for example, placing three rhombuses over one hexagon to show equality). Students count how many of each shape make one hexagon and write fractions with the hexagon as the whole (e.g., 1 triangle = 1/6, 3 triangles = 3/6, 1 rhombus = 1/3, 2 rhombuses = 2/3). The activity also asks students to treat different shapes as the whole (e.g., if the rhombus is one whole, what fraction is 1 triangle? = 1/2), requiring students to relate sizes of fractional parts across different wholes.

Students use a geoboard to create a 6 by 6 square and divide it into halves in three different ways (diagonal, vertical, horizontal), naming each part one-half. Students partition a 2 cm by 6 cm rectangle into thirds and name one part one-third, and the skills list asks students to 'express the area of each part as a unit fraction of the whole.' The unit test problems require students to divide shapes into equal parts, shade specified parts, and write the fraction of the whole that is shaded (examples: 2/4, 2/5, 2/3).

Students compute fractional parts of a scaled picture unit (e.g., identifying that one whole apple icon represents 10 apples and that half an apple represents 5). Students convert totals to pictograph units and mixed numbers (e.g., 30 apples -> 3 icons; 65 apples -> 6 and 1/2 icons; 85 games -> 4 and 1/4 icons). Students use a key where each symbol equals a fixed number (each square = 5 books) and create scaled pictographs, including showing partial symbols to represent non-whole multiples of the key.

Students practice labeling fractional marks (1/4, 1/2, 3/4, 1 1/4, 1 1/2, 1 3/4) on a number line and then measure items (lines and straw pieces) to those fractional positions. Students place Xs on a line plot at fractional points to record measured lengths, so they locate fractions as points on a number line. The introduction explicitly tells students that one-quarter is half of one-half and that it takes two quarters to make a half.

Students color and identify multiple fractions equal to one-half, one-third, two-thirds, and one-fourth on a laminated fraction chart (1/2, 2/4, 3/6, etc.). Students draw pictures on grid paper to prove that 1/2 and 2/4 are the same size and are reminded that equivalent fractions require the same-sized whole. Students also represent a fraction (two-thirds) on a number line in Activity 1.

Students are asked to divide a rectangle of 15 square centimeters into thirds, shade one-third, and show two-thirds, including finding another way to divide into thirds so parts are equal in area. The Skills section tells students to "Divide shapes into parts with equal areas and express each area as a fraction of the whole." Students also complete tasks to draw one-fourth of a 16-sq-cm square and two-thirds of a 9-sq-cm square, practicing fractional parts of shapes.