Math - Fourth Grade

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Fourth
Instructional Tasks

Stand alone tasks are organized to support learning of content standards. These tasks can be used as initial instruction or to support students who are struggling with a particular topic.

 

Strand: Mathematical PRACTICES (4.MP)
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Strand: OPERATIONS AND ALGEBRAIC THINKING (4.OA)
Use the four operations with whole numbers (addition, subtraction, multiplication, and division) to solve problems (Standards 4.OA.1–3).
  • Carnival Tickets
    This activity gives students a chart showing how the price of carnival tickets has increased over the years. They must answer questions using the table data. The purpose of this task is for students to solve multi-step problems in a context involving a concept that supports financial literacy, namely inflation.
  • Chessboard Algebra and Function Machines
    This Teaching Channel video shows how students can find the rule that determines the number of chessboard squares. (6 min.)
  • Comparing Money Raised
    The purpose of this task is for students to solve three comparisons problems that are related by their context but are structurally different. In these multiplicative comparison problems, one factor and the product are amounts of money and the other factor represents the number of times bigger one amount is than the other.
  • Karl's Garden
    Students are given this task: "Karl's rectangular vegetable garden is 20 feet by 45 feet, and Makenna's is 25 feet by 40 feet. Whose garden is larger in area?" The purpose of the task is for students to solve a multi-step multiplication problem in a context that involves area.
  • Thousands and Millions of Fourth Graders
    Students are given facts about the number of fourth graders in different places and asked to make calculations comparing the numbers. The purpose of this task is to help students understand the multiplicative relationship between commonly used large numbers (thousands and millions) by using their understanding of place value.
  • Threatened and Endangered
    Given facts about two endangered and threatened animals students are asked a question requiring them to understand multiplying and dividing whole numbers by powers of 10.
Gain familiarity with factors and multiples (Standard 4.OA.4).
  • Identifying Multiples
    Students are given a multiplication table for single digit numbers and asked to color all numbers with specific multiples. The goal of this task is to work on finding multiples of some whole numbers.
  • Multiples of 3, 6, and 7
    This task investigates divisibility properties for the numbers 3, 6, and 7. Students first make a list of multiples of 3 and then investigate this list further, looking for multiples of 6 and 7.
  • Numbers in a Multiplication Table
    The goal of this task is to encourage students to study the multiplication table, a familiar object, from a novel point of view. The table shows some, but not necessarily all, factorizations of different numbers. Working through the table to see where different numbers appear, the students will have a good opportunity to observe the symmetry of the table which comes from the commutative property of multiplication.
  • The Locker Game
    The purpose of this instructional task is for students to deepen their understanding of factors and multiples of whole numbers.
Generate and analyze numeric and shape patterns (Standard 4.OA.5).
  • Chessboard Algebra and Function Machines
    This Teaching Channel video shows how students can find the rule that determines the number of chessboard squares. (6 min.)
  • Double Plus One
    This task is meant to be used in an instructional setting. Part (b) of this task is intentionally left open-ended to encourage students to develop the habit of looking for patterns that might hint at some underlying structure as described in Standard for Mathematical Practice 7, Look for and make use of structure.
  • Multiples of 3, 6, and 7
    This task investigates divisibility properties for the numbers 3, 6, and 7. Students first make a list of multiples of 3 and then investigate this list further, looking for multiples of 6 and 7.
  • Multiples of Nine
    This task asks the students to start with 9 and list the first 10 multiples of 9. They are asked "In the list in part (a) what patterns do you see with the digits in the 10's place? What patterns do you see with the digits in the 1's place?" Using pictures, words, or equations, they must explain the patterns observed in part (b).
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Strand: NUMBER AND OPERATIONS IN BASE TEN (4.NBT)
Generalize place value understanding for multi-digit whole numbers by analyzing patterns, writing whole numbers in a variety of ways, making comparisons, and rounding (Standards 4.NBT.1–3).
  • Ordering 4-digit Numbers
    This task includes three-digit numbers with large hundreds digits and four-digit numbers with small thousands digits so that students must infer the presence of a 0 in the thousands place in order to compare. It also includes numbers with strategically placed zeros and an unusual request to order them from greatest to least in addition to the more traditional least to greatest.
  • Rounding on the Number Line
    This task helps students understand the concept of rounding by using the number line to illustrate how to find the closest benchmark numbers.
  • Rounding to the Nearest 100 and 1000
    Part (a) of this task fits squarely within third grade when students "use place value understanding to round whole numbers to the nearest 10 or 100". Part (b) is a first step in rounding beyond tens and hundreds.
  • Rounding to the Nearest 1000
    The purpose of this task is for students to estimate the position of numbers less than 10,000 on the number line, to practice rounding, and to make the connection between rounding and location on the number line.
  • Thousands and Millions of Fourth Graders
    Students are given facts about the number of fourth graders in different places and asked to make calculations comparing the numbers. The purpose of this task is to help students understand the multiplicative relationship between commonly used large numbers (thousands and millions) by using their understanding of place value.
  • Threatened and Endangered
    Given facts about two endangered and threatened animals students are asked a question requiring them to understand multiplying and dividing whole numbers by powers of 10.
Use place value understanding and properties of operations to perform multidigit addition, subtraction, multiplication, and division using a one-digit divisor (Standards 4.NBT.4–6) Expectations in this strand are limited to whole numbers less than or equal to 1,000,000.
  • Mental Division Strategy
    The task presents the scenario where Jillian says "I know that 20 times 7 is 140 and if I take away 2 sevens that leaves 126. So 126 ÷ 7 = 18." Students must then respond to this statement by answering if she's correct, drawing a picture showing her reasoning and using that method to solve another problem.
  • Reasoning About Division
    The Common Core allows students to get a better understanding of Math concepts and skills, including division. This Teaching Channel video shows how you can teach reasoning about division in your classroom. (7 min.)
  • Thousands and Millions of Fourth Graders
    Students are given facts about the number of fourth graders in different places and asked to make calculations comparing the numbers. The purpose of this task is to help students understand the multiplicative relationship between commonly used large numbers (thousands and millions) by using their understanding of place value.
  • To Regroup or Not to Regroup
    This task presents an incomplete problem and asks students to choose numbers to subtract (subtrahends) so that the resulting problem requires different types of regrouping.
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Strand: NUMBER AND OPERATIONS - FRACTIONS (4.NF)
Extend understanding of equivalence and ordering of fractions (Standards 4.NF.1–2)
  • Comparing Fractions Using Benchmarks Game
    The goal of this task is to determine appropriate benchmarks for fractions with a focus on providing explanations that demonstrate deep conceptual understanding.
  • Comparing Fractions with Lines
    This lesson will help students simplify fractions, compare and order them on a number line, and estimate their value.
  • Doubling Numerators and Denominators
    The purpose of this task is to assess whether students understand the meaning of the numerator and the denominator in a fraction. This task is not appropriate for a high-stakes summative assessment, but it could be very helpful in gauging students' flexibility with the meaning of fractions.
  • Explaining Fraction Equivalence with Pictures
    The purpose of this task is to provide students with an opportunity to explain fraction equivalence through visual models in a particular example.
  • Fraction King
    This is a lesson plan to help students compare two fractions and understand the addition and subtraction of fractions.
  • Fractions and Rectangles
    The primary goal of this task is for students to use pictures to explain the equivalence between 3/12 and 1/4.
  • IXL Game: Add and Subtract Fractions
    This game helps fourth graders understand how to compare two fractions with different numerators and different denominators. This is just one of many online games that supports the Utah Math core. Note: The IXL site requires subscription for unlimited use.
  • Listing fractions in increasing size
    This activity asks students to order a group of fractions from smallest to largest and explain their reasoning.
  • Rational Number Project
    This portal leads to 28 lesson plans designed to help students understand the four operations with fractions.
  • Using Benchmarks to Compare Fractions
    This task is intended primarily for instruction. The goal is to provide examples for comparing two fractions, 1/5 and 2/7 in this case, by finding a benchmark fraction which lies in between the two.
Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers (Standards 4.NF.3–4)
  • Addition of Fractions Using a Visual Model
    Adding two fractions with unlike denominators is the focus of this video lesson. Students will learn how to use a visual model to work with these fractions. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
  • Comparing Fractions with Lines
    This lesson will help students simplify fractions, compare and order them on a number line, and estimate their value.
  • Comparing Sums of Unit Fractions
    The purpose of this task is to help develop students' understanding of addition of fractions; it is intended as an instructional task.
  • Comparing Two Different Pizzas
    Students are given the example of two whole pizzas, one large and one medium. They must determine what fraction of the two pizzas has been eaten if someone eats 2 slices of the medium pizza. They must explain their reasoning and draw a picture to illustrate their solution.
  • Cynthia's Perfect Punch
    The purpose of this task is for students to estimate and compute sums of mixed numbers in the context of a student making a punch recipe.
  • Extending Multiplication From Whole Numbers to Fractions
    This task can be used at the beginning of a fourth grade unit on multiplication with fractions to evaluate what students know about multiplication.
  • Fraction King
    This is a lesson plan to help students compare two fractions and understand the addition and subtraction of fractions.
  • Rational Number Project
    This portal leads to 28 lesson plans designed to help students understand the four operations with fractions.
  • Sugar in Six Cans of Soda
    In this task students are given the statement "For a certain brand of orange soda, each can contains 4/15 cup of sugar." They are asked to calculate how many cups of sugar are in six cans and then draw a picture representing the answer.
  • What Fraction of this Shape is Red?
    This Teaching Channel video shows how students can explore part and whole by creating pattern block designs. (4 minutes)
Understand decimal notation to the hundredths and compare decimal fractions with denominators of 10 and 100 (Standards 4.NF.5– 7). Denominators for fourth grade are limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100.
  • Dimes and Pennies
    This task asks: "A dime is 1/10 of a dollar and a penny is 1/100 of a dollar. What fraction of a dollar is 6 dimes and 3 pennies? Write your answer in both fraction and decimal form."
  • Expanded Fractions and Decimals
    The purpose of this task is for students to show they understand the connection between fraction and decimal notation by writing the same numbers both ways.
  • Fraction Equivalence
    Students are given this task: "Explain why 6/10=60.100. Draw a picture to illustrate your explanation."
  • Rational Number Project
    This portal leads to 28 lesson plans designed to help students understand the four operations with fractions.
  • Using Place Value
    Each part of this task highlights a slightly different aspect of place value as it relates to decimal notation. More than simply being comfortable with decimal notation, the point is for students to be able to move fluidly between and among the different ways that a single value can be represented and to understand the relative size of the numbers in each place.
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Strand: MEASUREMENT AND DATA (4.MD)
Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit (Standards 4.MD.1–2)
  • Margie Buys Apples
    This task gives students an opportunity to work with familiar fractions and decimals in a context involving money.
  • Who is the tallest?
    In this task students are given a chart showing a list of students and their heights. They are asked to list the students from tallest to shortest.
Apply knowledge of area and perimeter to solve realworld and mathematical problems (Standard 4.MD.3)
  • Karl's Garden
    Students are given this task: "Karl's rectangular vegetable garden is 20 feet by 45 feet, and Makenna's is 25 feet by 40 feet. Whose garden is larger in area?" The purpose of the task is for students to solve a multi-step multiplication problem in a context that involves area.
Represent and interpret data through the use of a line plot (Standard 4.MD.4)
  • Button Diameters
    The purpose of this task is for students to measure lengths to the nearest eighth and quarter-inch and to record that information in a line plot.
Understand various concepts of angles and angle measurement (Standard 4.MD.5–7)
  • Finding an Unknown Angle
    The purpose of this task is to give 4th grade students a problem involving an unknown quantity that has a clear visual representation. Students must understand that the four interior angles of a rectangle are all right angles and that right angles have a measure of 90∘ and that angle measure is additive.
  • Measuring Angles
    The purpose of this task is to gain experience drawing and measuring angles, developing an understanding of the additive structure of angles.
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Strand: GEOMETRY (4.G.)
Draw and identify lines and angles, as well as classify shapes by properties of their lines and angles (Standards 4.G.1–3)
  • An Introduction To Quadrilaterals
    In this lesson the student is introduced to parallelograms, rectangles, and trapezoids and practices creating various types of quadrilaterals.
  • Are These Right?
    The purpose of this task is for students to measure angles and decide whether the triangles are right or not.
  • Defining Attributes of Rectangles and Parallelograms
    The purpose of this task is for students to identify the defining attributes of rectangles and parallelograms. This task should be completed after students have many experiences sorting shapes by attributes.
  • Finding Lines of Symmetry
    The purpose of this task is for students to identify figures that have line symmetry and draw appropriate lines of symmetry.
  • Finding an Unknown Angle
    The purpose of this task is to give 4th grade students a problem involving an unknown quantity that has a clear visual representation. Students must understand that the four interior angles of a rectangle are all right angles and that right angles have a measure of 90∘ and that angle measure is additive.
  • Geometry of Letters
    The purpose of this task is for students to analyze the geometry of letters. Letters provide a good opportunity for students to broaden their understanding of what constitutes a 2-dimensional geometric figure.
  • Lines of symmetry for circles
    This is an instructional task that gives students a chance to reason about lines of symmetry and discover that a circle has an an infinite number of lines of symmetry.
  • Lines of symmetry for quadrilaterals
    This task provides students a chance to experiment with reflections of the plane and their impact on specific types of quadrilaterals.
  • Lines of symmetry for triangles
    This task is intended for instruction, providing the students with a chance to experiment with physical models of triangles, gaining spatial intuition by executing reflections.
  • Measuring Angles
    The purpose of this task is to gain experience drawing and measuring angles, developing an understanding of the additive structure of angles.
  • What Shape am I?
    In this task, students ultimately use the definitions they are given for three types of quadrilaterals and what they know about parallel sides to identify that a square fits all the definitions and explain why.
  • What is a Trapezoid? (part 1)
    The purpose of this task is for students to articulate a definition for a trapezoid. After students have articulated definitions for themselves or with a partner, the class should discuss the definition together.
  • What's the Point?
    The purpose of this task is to use what students intuitively understand about connecting points or "dots" with lines to generate a discussion about what points are and how they should be represented.
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