Third Grade - MATH
5: Math
Unit 1: Multiplication and Division I
Lesson 14
Multiplication and Division Fact Families
Students model division with 20 counters, physically partitioning a whole of 20 into 4 equal groups of 5 and into 5 equal groups of 4 while writing 20÷4=5 and 20÷5=4. Students create multiplication and division fact families (e.g., 3, 4, 12) and write corresponding division sentences that show the largest number being partitioned into equal groups (12÷3=4, 12÷4=3).
Unit 3: Measurement
Lesson 1
Practice With Time
Students identify and work with half hours and quarter hours by answering questions such as "How many minutes are in a half hour?" (30) and "How many quarter hours make up an hour?" (4). Students read and show times like "half past 6," "a quarter to 8," and 7:30 on geared and blank clock faces, and they draw hour and minute hands for times such as 7:30 and 8:45. Students use the minute hand position (e.g., pointing to the 3 for 15 minutes) to reason about portions of an hour when rounding and estimating time.
Lesson 3
Elapsed Time
Students partition hours into quarters by marking :15, :30, and :45 and are asked to label quarter-hour marks on number lines and clocks. Students identify :30 as halfway between hours and are referred to "two and a half hours," equating 30 minutes with a half hour. Students draw arcs and label intervals as 1 hour, 30 minutes, 15 minutes when decomposing elapsed time on number lines.
Lesson 5
More Work With Weight
Students use examples where a whole pound is partitioned into equal items (e.g., "These 4 bananas together weigh 1 pound," "It takes 168 ping pong balls to make a pound," and a bag of rice weighs 1 pound). Students compute how many of those unit items equal their weight by multiplying (e.g., pounds × 4 for bananas) or dividing (e.g., student weight ÷ item weight for items heavier than a pound). These tasks require treating an individual item as a consistent part of a whole pound.
Lesson 6
Exploring Volume
Students use a 1-cup measure to fill pint, quart, and gallon containers and count the equal parts to find that 1 pint = 2 cups, 1 quart = 4 cups, and 1 gallon = 16 cups. Students create and assemble a foldable that stacks cups, pints, quarts, half-gallons, and gallons to visualize how a gallon is partitioned into smaller equal units. Students answer questions such as "How many half gallons are in one whole gallon?" and measure containers by counting unit cups.
Lesson 7
More Work With Volume
Students fill a 10-milliliter syringe, count milliliters from 1 to 10, and add 10 ml ten times to make 100 ml, showing repeated equal parts of a unit. Students pour 100-ml portions into a 1-liter container and keep tally marks, discovering that it takes ten equal 100-ml pours to make 1000 ml (1 liter). Students match representations (20 drops = 1 ml and 1000 ml = 1 liter) on activity pages, reinforcing that specific equal-size parts combine to form a larger whole.
Lesson 9
Unit Test
Students are asked to set and say times such as "half past 3," "a quarter after 6," and "a quarter to 11," and to state those times in more than one way (for example, "half past three" and "three thirty"). Students use a geared clock to show specified times and answer questions about times rounded to the nearest hour and time intervals (e.g., what time will it be in 30 minutes?).
Unit 4: Multiplication and Division II
Final Project
Planning a Picnic
Students divide 24 children into teams of 4 for the egg toss and compute there will be 6 teams, and they divide all participants into 5 groups for the sack race and compute 12 people per group. Students use division to determine how many bags of chips are needed (one bag serves 12 people) and to compute numbers of packages for supplies based on 60 people. Students use the seating-arrangement activity to partition 60 people into parts (blankets seat 4, small tables seat 6, large tables seat 10) and choose combinations that sum to 60.
Unit 5: Area and Perimeter
Lesson 1
Review of Plane Shapes
The lesson asks students to use a ruler and reminds them how to find a half-inch mark, and it requires students to draw and measure lines that include half-inch amounts (e.g., 2 and a half inches, 5 and a half inches, 9 and a half inches). The measuring tasks and answer key show specific fractional lengths (b=3 in., c=5 in., d=1 in.; and n=5 cm, x=8 cm, y=3 cm) and include explicit practice locating and using .5-inch marks on the ruler.
Unit 6: Fractions
Lesson 1
What Is a Fraction?
Students cut an apple into 2, 4, 8, and other equal parts and name single parts as one-half, one-fourth, and one-eighth, explicitly showing 1/b as one part of a partitioned whole. Students use a geoboard to divide a square into thirds, ninths, halves, and quarters and are asked to point to and name one-third, one-ninth, two-ninths, and three-ninths. Students complete shape-coloring activities and are told that the second number (denominator) tells how many equal parts the whole is divided into and the first number (numerator) tells how many of those parts are selected.
Lesson 2
Naming Fractions
The lesson explicitly defines numerator and denominator and lists as a skill: "Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts" and "Understand a fraction a/b as the quantity formed by a parts of size 1/b." Students repeatedly name and match written fractions to shaded visual models in activities (Matching Fractions, Naming Fractions) and answer questions that require identifying unit fractions (e.g., which fractions have numerator 1). Students color circles divided into equal parts and then write the fraction for each color, directly linking shaded equal parts to 1/b and a/b representations.
Lesson 3
Fraction Parts
The Skills section explicitly states the target idea: understanding 1/b as one part of a whole partitioned into b equal parts and a/b as a parts of size 1/b. In the Getting Started and Activities, students create and count colored tiles to name fractions (e.g., 6 out of 10) and label numerator and denominator. In Activities 2–4 students build and use fraction strips, shade parts with interactive tools (showing 1/12, 7/8, 10/12, etc.), and keep the numerator fixed at 1 while changing the denominator to observe that parts get smaller.
Lesson 4
More Fraction Exploration
Students use the interactive geoboard to show fractions (1/2, 3/4, 5/12) and point to or shade equal parts of a whole. In Activity 1 they write unit fractions, identify that unit fractions have numerator 1, and build a stair of fraction strips showing 1, 1/2, 1/3, ... 1/16 so they compare sizes of single parts. Activity 2 and the apple/pizza examples have students partition a whole into equal parts, name 1/4, 2/4, 3/4, 4/4 and interpret 4/4 as one whole, and Activity 3 has students place multiple fraction strips (1/2, 1/4, 1/8) to form one whole demonstrating a/b as a parts of size 1/b.
Lesson 5
Fractions, Division, and Groups
Students cut and color fraction circles and use them to share one pizza among two, three, and four people, explicitly labeling 1/2, 1/3, and 1/4 and pointing to the numerator and denominator. Students divide counters into equal groups (12 counters into 2, 3, 4, and 6 groups) and name each group as one-half, one-third, one-fourth, and two-sixths, showing parts of the whole. Students create designs and complete worksheets that require counting the total tiles (denominator) and counting specific colored parts (numerator) and writing fractions (e.g., 3/5, 2/6) and corresponding division statements (e.g., 3 divided into 5 groups).
Lesson 6
Fractions on Number Lines
The Skills list explicitly states students will understand 1/b as one part of a whole partitioned into b equal parts and a/b as a parts of size 1/b, and it describes representing these on a number line. Activities ask students to identify denominators and numerators by counting spaces on number lines, match labeled points to fractions, and plot fractions such as 1/3, 2/6, and 3/10. Activity 3 has students construct number lines (halves, eighths, twelfths), mark equal partitions, and move to positions 1/8, 2/8, etc., which requires marking off a lengths of 1/b from 0 to locate a/b.
Lesson 7
Equivalent Fractions
Students partition and compare wholes in multiple activities: they place fraction strips and fraction circles to show 1/2, 2/4, and 4/8 and overlay halves to show equal size. In Activity 3 they draw three identical rectangles, divide them into 2, 4, and 8 equal parts, and shade 1/2, 2/4, and 4/8 so the colored regions match. The student pages and exercises ask students to color sections to represent fractions and to complete equations such as 1/2 = □/4, 1/3 = □/6, and other missing-number equivalences. Games and matching activities require students to match visual partitions with numeric fractions (e.g., Triplets, Fraction Matcher, Fraction Dominoes).
Lesson 8
Fractions in Our World
The Skills section explicitly states that students will "Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b." In Activity 1 students partition an hour into 12 equal five-minute parts and write fractions for times (e.g., 10 minutes = 2/12, 45 minutes = 9/12 = 3/4). In Activity 3 students color beads on bracelets to represent unit fractions and compose a/b by counting colored beads, and Activity 2 has students represent coins as fractions of a dollar (quarter = 1/4, half-dollar = 1/2).
Lesson 9
Unit Test
The Skills section explicitly restates the standard language and students are asked to draw pictures representing one-half, one-fourth, and one-third, which requires partitioning a whole into equal parts. Introductory questions ask students what the numerator and denominator are and what each represents, linking the numerator to parts and the denominator to total equal parts. Tasks have students divide a number line into five equal parts and place 3/5, and students identify unit fractions (1/3) and that 3/3 equals one whole, showing a/b as a collection of 1/b parts.
Final Project
Fraction BINGO
The Skills list explicitly states the target understanding (1/b as one part of a whole partitioned into b equal parts and a/b as a parts of size 1/b). In Step 3 students are asked to complete visual fraction models by shading parts of circles and squares and by placing colored dots on number lines, and the BINGO Card Spaces include rows showing fractions (e.g., 1/2, 2/3, 3/8, 5/8) in visual, word, and number forms. Step 4 directs students to keep same-fraction examples together and place one example of each fraction on each card, and Step 7 asks students to explain to others how clocks, coins, and number lines show fractions.
Unit 7: Geometry
Lesson 6
Dividing Shapes
Students use geoboards and grids to partition wholes into equal parts and are asked to name each part as a unit fraction (Activity 1: students create halves, quarters, eighths and write 1/2, 1/4, 1/8). In Activity 2 students divide a 9×9-square into nine equal squares, shade one-ninth and then shade three-ninths, and are asked what the numerator and denominator represent. In Activity 3 students divide a 3×4 rectangle into halves, thirds, and fourths, compute how many square centimeters each unit fraction represents, and create multiple equal-area divisions showing that a/b can be formed by several 1/b parts.
Lesson 7
Some Geometric Problem Solving
Students divide a hexagon into equal trapezoids, rhombuses, and triangles and count how many of each make one whole. Students name unit fractions explicitly (for example, 1 trapezoid = 1/2, 1 rhombus = 1/3, 1 triangle = 1/6) and label multiples of those parts (for example, 2 trapezoids = 2/2, 3 triangles = 3/6). The skills and activity instructions ask students to partition shapes into equal areas and express the area of each part as a unit fraction of the whole.
Lesson 8
Unit Test
The Skills section tells students to "Partition shapes into parts with equal areas" and to "Express the area of each part as a unit fraction of the whole." In activities, students use a geoboard to create a 6x6 square and divide it into halves and fourths while naming each part "one-half," and they divide a 2 cm by 6 cm rectangle into thirds and name one part "one-third." The Unit 7 Test problems (8–11) require students to divide shapes into 3, 4, or 5 equal parts, shade a specified number of parts, and write the fraction shaded (e.g., 2/4, 2/5, 2/3).
Unit 8: Graphing Data
Lesson 2
Pictographs
Students are asked to identify the value of one picture in a scaled pictograph (e.g., one apple image represents 10 apples) and to explain why half or a quarter of that picture equals a specific number (half an apple equals 5; a quarter of a tennis ball equals 5 when a whole equals 20). Students interpret and produce mixed pictorial values (e.g., 65 apples shown as 6 and 1/2 apple icons; 85 tennis games as 4 and 1/4 tennis balls). Students create their own pictographs with a stated scale and must show partial pictures when counts are not exact multiples of the scale (instructions and answer key show squares representing 5 books and partial squares for remainders).
Lesson 3
Bar Graphs
The Basic Skills Review #23 asks a fraction identification question with a shaded rectangle (answer: 7/10), which requires students to recognize parts of a whole. The same review also includes a fraction comparison item, asking which is greater, 3/8 or 6/8 (answer: 6/8), which has students interpret numerators as counts of equal-sized parts.
Lesson 4
Line Plots
Students are asked to locate the half-inch and quarter-inch marks on a ruler and are asked explicitly how many half inches are in a whole inch. Students are reminded that one-quarter is half of one-half and are guided to label the marks 1/4, 1/2, 3/4 and the fractional marks between 1 and 2 (1 1/4, 1 1/2, 1 3/4). Students measure straw pieces and record lengths as fractions and mixed numbers (for example, 3 1/4, 4 1/2, 5 1/2) and then place Xs on a line plot above the corresponding fractional marks. The measuring and labeling activities require students to treat 1/b as one part of an inch and a/b (or mixed numbers) as multiple such parts.
Lesson 5
More Work With Graphing
Students answer a Basic Skills Review question that asks them to identify the fraction not shaded in a divided circle, requiring them to interpret parts of a whole. Students also answer a comparison question (Which is greater, 5/7 or 6/7?), which requires understanding fractions as quantities with the same-sized parts. The lesson includes a web activity titled "Create Line Plots With Fractions," where students complete 10 practice questions using line plots that involve fractional values.
Lesson 6
Unit Test
Students identify missing fractional tick marks on a line plot (they are asked to note 1/2, 2, and 2 1/2). Students place Xs on a line plot to record growth amounts given as fractions and mixed numbers (e.g., 1/2, 1, 1 1/2, 2, 2 1/2, 3). Students answer unit-test items that require recognizing and reading fractional labels (e.g., identifying A as 1/2, B as 1 1/4, C as 2; and answering how many people spent 1/2 hour or 3/4 hour practicing guitar).
Unit 9: Skills Review
Lesson 2
Reviewing Fractions
Students are asked to write the fraction two-thirds as 2/3 and to draw a circle or square divided into three parts with two parts shaded, and to mark two-thirds on a number line divided into three equal spaces. Students color and identify sets of fractions equal to one-half (1/2, 2/4, 3/6, etc.) and are instructed to draw pictures on same-size shapes to prove that 1/2 and 2/4 represent the same amount. Students also order and compare simple fractions (e.g., 1/2, 1/3, 1/4) and circle the larger fraction in paired comparisons, using matching shapes or number-line representations as needed.
Lesson 4
Reviewing Geometry
Students draw a rectangle of 15 square centimeters and divide it into thirds, shading one-third and showing two-thirds so each third has five square units. Students are asked to find another way to divide the same rectangle into three equal-area parts, emphasizing that each part must be the same size in area. Students also work problems asking for one-fourth of a 16-square-centimeter square and two-thirds of a 9-square-centimeter square, and they identify coin fractions (one-fourth, one-tenth, one-twentieth) in the introduction.