Third Grade - MATH
5: Math
Unit 6: Fractions
Lesson 1
What Is a Fraction?
Students divide shapes into equal parts using manipulatives: they use a geoboard to make a circle and split it into two and four equal pieces (halves and quarters), create a large square and divide it into thirds and into nine equal squares (thirds and ninths), and fold paper to make halves, fourths, and eighths. Students name each equal part verbally as unit fractions (one-half, one-third, one-fourth, one-ninth, one-eighth) and practice identifying two-ninths and three-ninths. Activities ask students to color and identify fractions of shapes and to consider area (how much space something takes up) when comparing wholes and parts.
Lesson 2
Naming Fractions
The Skills section explicitly states students should "understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts". In Activity 1 students count shaded parts of circles (e.g., point to a circle showing one-fourth and say "one out of four parts shaded") and match shaded diagrams to fraction names. In Day 2 (Colorful Circles) students color specified numbers of equal parts of circles and write the corresponding fractions (e.g., 1/4, 3/4, 2/8).
Lesson 3
Fraction Parts
Students work with the explicit definition that 1/b is one part when a whole is partitioned into b equal parts and that a/b is a parts of size 1/b. Students fold and label fraction strips to create wholes, halves, fourths, and eighths, physically partitioning a strip into equal-area parts and writing 1, 1/2, 1/4, 1/8 on them. Students use interactive shape tools and coloring activities to partition and shade circles, squares, and pizzas to show specified fractions such as 1/12, 7/8, and 10/12.
Lesson 4
More Fraction Exploration
Students use the circle geoboard to partition a circle and show fractions such as 1/2, 3/4, and 5/12, explicitly creating equal-area slices. Students use the interactive pizza tool to set a denominator (e.g., 8) and click equal pizza pieces to show 8/8 and other unit-fraction parts. Students manipulate and arrange fraction strips and a fraction chart to make wholes and to see that 1/b represents one equal part when the whole is partitioned into b equal parts (e.g., asking how many eighths make a whole and covering the whole with strips).
Lesson 5
Fractions, Division, and Groups
Students cut and shade fraction circles into halves, thirds, and fourths and use those pieces to model sharing pizzas, labeling each share as 1/2, 1/3, or 1/4. Student activity pages show circles divided into 2, 3, and 4 equal sections and a table of shapes divided into 5, 6, 8, 5, and 10 equal parts with shaded regions that students translate into fractions (e.g., 3/5, 2/6). In Activity 2 students complete a "Shapes, Fractions, and Division" sheet by identifying equal parts of shapes and writing the corresponding unit fractions and division statements.
Lesson 6
Fractions on Number Lines
Students partition the interval from 0 to 1 into equal parts on number lines (Activity 3) and practice identifying and plotting fractions such as 1/3, 2/6, and 3/10 (Activities 1 and 3). Students match fractions to shaded visual models and number-line positions in the "More Fraction Matching" and other matching activities, and they answer questions about equivalence (e.g., 4/8 and 5/10 are the same).
Lesson 7
Equivalent Fractions
Students partition and shade fraction circles and fraction strips to show 1/2, 2/4, 4/8 and color corresponding sections on a laminated fraction chart. Students draw three equal-size rectangles and divide them into 2, 4, and 8 equal parts, shading specified numbers of parts so the colored regions look the same. Students complete worksheets and missing-number problems that record equivalences (e.g., 1/2 = __/4, 1/3 = __/6) and play matching games that pair partitioned shapes with numeric fractions.
Lesson 8
Fractions in Our World
The lesson explicitly states the key fraction definition: "Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts." Students move the geared clock and answer questions that partition an hour into 12 five-minute parts and into quarters (e.g., 2/12, 9/12 = 3/4, 1/4 = 15 minutes). Students color and count beads on "Fraction Bracelets" to create and record fractional parts (e.g., 1/2 orange, 1/4 blue, 1/4 yellow) and design their own bracelets showing fractions. The introduction gives real-world partition examples such as "half of a pie" and other everyday fractional parts.
Lesson 9
Unit Test
Students are asked to draw pictures (circles, squares, groups of objects) to represent one-half, one-fourth, and one-third, which requires partitioning shapes into equal parts. The Skills section explicitly states understanding 1/b as the quantity formed when a whole is partitioned into b equal parts and understanding a/b as a parts of size 1/b. Unit Test items and activity pages ask students to identify what fraction shaded images show, identify images equal to one-half, and name fractions shown in diagrams, requiring interpretation of partitioned shapes as unit fractions.
Final Project
Fraction BINGO
The Skills section explicitly states students should "understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts," and to "understand a fraction a/b as the quantity formed by a parts of size 1/b." Step 3 directs students to complete representations by shading parts of circles and squares and placing colored dots on number lines to show given fractions. Several Student Activity Page descriptions show shapes divided into equal parts (e.g., a circle divided into five sections, rectangles divided into equal parts) and ask students to label those representations in words and numeric fraction form (e.g., "one-fifth," "1/5").
Unit 7: Geometry
Lesson 6
Dividing Shapes
Students use geoboards to create the largest square and are asked to divide it into 2, 4, and 8 equal parts and to name each part as 1/2, 1/4, and 1/8. Students draw a 9 cm square and divide it into nine equal squares, shade one-ninth and then shade additional ninths writing fractions like 3/9 and explaining numerator and denominator. In Activity 3 students divide a 3×4 rectangle into halves, thirds, and fourths by area (counting square centimeters) and are asked to show multiple ways to create equal-area parts; student pages and complex-shape sheets require dividing shapes into specified equal parts and shading the indicated unit fractions.
Lesson 7
Some Geometric Problem Solving
The Skills list explicitly states that students will "Partition shapes into parts with equal areas" and "Express the area of each part as a unit fraction of the whole." Activity 1 and the Student Activity Page have hexagon models divided into trapezoids, rhombuses, and triangles and ask students to count how many of each shape make one hexagon. The activity directs students to name parts as fractions (for example, 1 trapezoid = 1/2, 1 rhombus = 1/3, 1 triangle = 1/6), showing partitioning into equal-area parts and expressing each part as a unit fraction.
Lesson 8
Unit Test
The Skills list explicitly includes both "Partition shapes into parts with equal areas" and "Express the area of each part as a unit fraction of the whole." Students use a geoboard to create a 6 by 6 square and divide it into halves and fourths while naming each part (one-half, then one-fourth). Students create a 2 cm by 6 cm rectangle and divide it into thirds, naming one-third. Unit Test items 8–11 ask students to divide given shapes into equal parts and record the fraction of the whole that is shaded (e.g., divide into 4 equal parts and shade 2 parts → 2/4).
Unit 8: Graphing Data
Lesson 2
Pictographs
Students interpret halves and quarters of pictograph symbols when answering questions such as "Why does half of an apple equal 5?" and "Why does a quarter of the tennis ball represent 5?" The activity asks students to read and create scaled pictographs that include partial icons (e.g., representing 65 apples as 6 and 1/2 apples and 85 games as 4 and 1/4 tennis balls). The Library Pictograph answer key and graph templates show a key where each square represents 5 books and include partial squares to represent non-multiples of the scale.
Unit 9: Skills Review
Lesson 2
Reviewing Fractions
Students are asked to write the fraction two-thirds in numeric form and to draw a circle or square divided into three parts with two parts shaded, showing partitioning of a shape into equal-area parts. Students draw number-line representations of fractions and order fractions such as 1/2, 1/3, and 1/4, which reinforces unit-fraction concepts. Students color grids and use a laminated fraction chart to mark all fractions equal to one-half, one-third, two-thirds, and one-fourth, and they draw pairs of same-size squares divided to show 1/2 and 2/4 are the same, providing visual partitioning and labeling of equal parts.
Lesson 4
Reviewing Geometry
Activity 2 asks students to draw a 15 cm² (3×5) rectangle, divide it into thirds, shade one-third, and note that each third is five 1 cm² squares. The activity also asks students to find another way to make equal thirds and to draw one-fourth of a 16 cm² square and two-thirds of a 9 cm² square. The Skills section explicitly states students should "Divide shapes into parts with equal areas and express each area as a fraction of the whole."