Third Grade - MATH
5: Math
Unit 3: Measurement
Lesson 6
Exploring Volume
Students determine and record equal measures of volume (e.g., finding that 2 cups = 1 pint, 4 cups = 1 quart, 8 cups = 1 half-gallon, 16 cups = 1 gallon) by filling and measuring containers (Activity 1, Activity 4). Students create a foldable that visually stacks cups, pints, quarts, half-gallons, and gallons to show how smaller units make up larger units, and they answer questions about how many half gallons are in a gallon and related unit relationships (Activity 2 and color/sort sheet).
Unit 6: Fractions
Lesson 1
What Is a Fraction?
Students partition shapes with the geoboard into halves, thirds, fourths, and ninths and name each part (e.g., "This is one-third"). The apple activity has students identify and name pieces such as "two-fourths or two-quarters." The "Showing Fractions in Shapes" activity has students color and identify fractions and includes examples labeled two-fourths, four-sixths, and four-eighths, and students choose which fractional label matches a shaded region.
Lesson 2
Naming Fractions
Students cut out and create pairs on the "Matching Fractions" activity that require them to match written fractions with visual models of the same amount. The "Naming Fractions" pages present both 2/3 and 4/6 with accompanying pie charts so students see the same quantity represented two ways. The "Colorful Circles" tasks ask students to color equal-part diagrams and write the fraction for each colored amount (e.g., 2/8, 4/8). The web activity (Fraction Matcher) directs students to identify fraction names and models that are the same by dragging images to match.
Lesson 3
Fraction Parts
Students make and use fraction strips (Activity 2 and "Make Your Own Fraction Strips") by folding strips into wholes, halves, fourths, and eighths and placing those pieces beneath each other. The lesson asks students to answer questions such as "How many fourths equal one half? (2)" and "How many eighths equal one half? (4)," and to shade parts with an interactive tool while changing denominators (Activity 3) so they can see equal amounts represented with different denominators.
Lesson 4
More Fraction Exploration
Students color and identify multiple fractions equal to one-half (Activity 5), writing examples such as 2/4, 3/6, 4/8, 5/10, and 6/12. Students use visual models throughout (laminated fraction chart, fraction strips, pizza interactive, geoboard) to show and compare parts and to stack strips to make wholes (Activity 3). Students are prompted to explain why those fractions are equivalent by noting relationships between numerators and denominators and by physically combining parts (apple, stacked strips) to show equality.
Lesson 5
Fractions, Division, and Groups
Students manipulate fraction chart pieces and are asked to identify and name pieces (e.g., one-ninth, eight-twelfths, 3/6, 4/6) and to reassemble visual fraction charts. Students use fraction circles to model sharing pizzas (showing 1/2, 1/3, 1/4 and modeling two pizzas shared as 2/3 and as 2/4) and point to numerators and denominators. Students create designs and use colored tiles to form specified fractional parts (tasks explicitly ask for 1/2, 1/4, 1/3, 1/5, etc.), providing repeated practice with visual fraction models.
Lesson 6
Fractions on Number Lines
Students are asked to match fractions on number lines and to plot fractions such as 1/3, 2/6, and 3/10, which gives practice locating equivalents like 2/6 and 1/3. The Think About It prompt explicitly asks what students notice about 4/8 and 5/10 and states they are the same (both are one-half of the line). The More Fraction Matching activity has students cut and match three cards showing the same fraction in different representations (fraction notation, shaded diagram, and number line), supporting visual explanations of equivalence.
Lesson 7
Equivalent Fractions
Students are instructed to show 1/2, 2/4, and 4/8 using fraction strips and to show 1/2 and 2/4 using fraction circles, then place one half on top of another and write 1/2 = 2/4. Students color equivalent fractions on a laminated fraction chart (e.g., 2/3, 4/6, 6/9, 8/12) and complete a worksheet that requires filling missing numerators/denominators for equivalent fractions. Students draw and shade three congruent rectangles partitioned into 2, 4, and 8 parts to demonstrate 1/2 = 2/4 = 4/8, and they practice matching/generating equivalent fractions with games and a Dominoes activity.
Lesson 8
Fractions in Our World
Students represent the same quantity using different fraction forms in several activities: the Fractions and Time activity asks students to write 45 minutes as 9/12 and 3/4 while using a geared clock as a visual model. The Fractions and Money chart has students write amounts as both x/100 and simplified fractions (for example 25/100 and 1/4, 50/100 and 1/2). The Fraction Bracelets activity has students color beads and compute counts that show equivalent fractions (e.g., 1/2 = 8/16, 1/4 = 4/16), providing visual bead models of equivalence.
Lesson 9
Unit Test
Students reassemble and use a laminated fraction chart to identify fractions equal to one-half and one-third and to find equivalents (e.g., 5/6 = 10/12, 3/5 = 6/10). Students lay out Fraction Dominoes to connect equivalent fractions shown in different ways and complete test items that ask which image is equivalent to a given fraction and to identify fractions equal to one-half. The materials instruct students to use fraction circles, fraction strips, and number lines when practicing and placing fractions (e.g., marking 3/5 on a number line).
Final Project
Fraction BINGO
Students complete BINGO Card Spaces that show each target fraction in multiple forms (words, circles, rectangles, number lines, clocks, coins) and are asked to shade parts of circles and squares and place dots on number lines to represent the given fractions. Students are instructed to keep images showing the same fraction together (e.g., all one-half examples) and to place one example of each fraction on each game card, varying the representation. Students are also asked to explain to other players how clocks, coins, and number lines can be used to show fractions before playing.
Unit 7: Geometry
Lesson 3
What Is a Quadrilateral?
The Basic Skills Review #20 item asks "What fraction is this?" showing a shaded rectangle, and the answer key lists that fraction as 2/6. This requires students to identify a fraction from a visual model. No other activities explicitly teach or practice generating or explaining equivalent fractions.
Lesson 6
Dividing Shapes
Students partition shapes into equal parts and label those parts with unit fractions (e.g., 1/2, 1/4, 1/8) when they create halves, fourths, and eighths on the geoboard and grids. Students divide a 9×9 square into nine smaller squares, shade one-ninth and later shade three-ninths (3/9), and complete tasks that require dividing shapes into six parts and shading two parts (2/6). Students use a 3×4 (12 square centimeter) rectangle to create halves, thirds, and fourths in multiple ways and are asked to show that the same whole can be divided in different ways so that parts have the same area.
Lesson 7
Some Geometric Problem Solving
Students use the Pattern Blocks interactive to place rhombuses, trapezoids, and triangles onto a hexagon (e.g., the instructions say to show that three rhombuses are the same as one hexagon). The Activity 1 answer key and Student Activity Page require students to count how many trapezoids, rhombuses, and triangles make one hexagon and to name those parts as fractions (e.g., 1 trapezoid = 1/2, 3 triangles = 3/6, 4 triangles = 4/6, 2 rhombuses = 2/3). Students are also asked to treat different pieces as the whole (e.g., if the rhombus is one whole, what fraction is 1 triangle? = 1/2), which uses the visual models to show equivalence.
Lesson 8
Unit Test
Students partition shapes into equal areas and express each part as a unit fraction of the whole (skills listed explicitly). Students use a geoboard to create a 6x6 square and divide it into halves in three different ways (diagonal, vertical, horizontal) and name each part "one-half," and they repeat the process for fourths. Students complete shading problems where they divide shapes into 3, 4, or 5 equal parts and write the fraction of the whole that is shaded (answers shown as 2/4, 2/5, 2/3, 2/5).
Unit 8: Graphing Data
Lesson 2
Pictographs
Students interpret scaled pictographs by identifying fractional parts of a picture unit (e.g., one apple picture represents 10 apples, so half an apple equals 5). Students determine quarters, halves, and three-fourths of a pictograph unit (e.g., a quarter of a tennis ball represents 5 when a full ball equals 20; three-fourths represents 15). Students represent mixed-number amounts on pictographs (e.g., 65 apples shown as 6 and 1/2 apple icons; 85 tennis games as 4 and 1/4 tennis balls).
Lesson 4
Line Plots
Students measure with a ruler marked in halves and quarters and are asked to identify the 1/2, 1/4, 3/4, and related fractional marks on a number line. The introduction explicitly reminds students that "one-quarter is half of one-half (it takes two quarters to make a half)," linking quarters and halves. In Activity 2 students label fractional marks on the line and place Xs for measured straw lengths such as 4 1/2, 3 1/4, and 1 1/2, using the number line/ruler as a visual reference.
Unit 9: Skills Review
Lesson 2
Reviewing Fractions
Students are asked to color all fractions equal to one-half on a laminated chart (1/2, 2/4, 3/6, 4/8, 5/10, 6/12) and to color equivalents for one-third, two-thirds, and one-fourth. Students are instructed to draw pictures on grid paper to "prove" that 1/2 and 2/4 are the same, and reminded that equivalents require the same-sized whole. Students also use a fraction-matching scale game and match fraction amounts (including pairs like 2/3 and 4/6) to verify equivalence.
Lesson 4
Reviewing Geometry
Students draw a rectangle of area 15 sq cm, divide it into thirds, shade one-third, and show two-thirds, which requires partitioning a whole into equal parts and naming parts as fractions. They are asked to find another way to divide the same rectangle into thirds, and to draw one-fourth of a 16-sq-cm square and two-thirds of a 9-sq-cm square, practicing multiple visual partitionings. The skills list and introductory money questions also ask students to express equal-area parts as fractions (e.g., quarter = one-fourth, dime = one-tenth).