 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 (3.MP) Strand: OPERATIONS AND ALGEBRAIC THINKING (3.OA)
Represent and solve problems involving multiplication and division within 100 (Standards 3.OA.1–4 and Standard 3.OA.7)
• Analyzing Word Problems Involving Multiplication
The purpose of this task is for students to analyze different contexts in which multiplication is appropriate.
• Classroom Supplies
In this task students are asked to decide how to spend \$1,000 on supplies and materials for their classroom; students will have to make choices and be careful not to exceed the budget. Students are asked to decide which supplies will benefit the class the most and will compare their choices with other students' choices.
• Finding the unknown in a division equation
This task shows an equation that elicits key misconceptions around equations and division. Students will be tempted to identify 3 as the missing number because they are envisioning the related fact: 6 / 2 = 3. Teachers using this task for discussion will want students to voice ideas leading to both answers, but guide the discussion to some key instructional point.
• Fish Tanks
The purpose of this task is to provide an opportunity for students to demonstrate that they can interpret within a given context the meaning of whole number quotients.
• Gifts from Grandma, Variation 1
The first of these is a multiplication problem involving equal-sized groups. The next two reflect the two related division problems, namely, "How many groups?" and "How many in each group?"
• Markers in Boxes
The purpose of this task is for students to compare two problems that draw on the same context but represent the two different interpretations of division, namely, the "How many groups?" interpretation and the "How many in each group?" interpretation.
• Two Interpretations of Division
This task asks students two questions: " Maria cuts 12 feet of ribbon into 3 equal pieces so she can share it with her two sisters. How long is each piece? Maria has 12 feet of ribbon and wants to wrap some gifts. Each gift needs 3 feet of ribbon. How many gifts can she wrap using the ribbon?"
They demonstrate understanding of the properties of multiplication and the relationship between multiplication and division (Standards 3.OA.5–6)
• Valid Equalities? (Part 2)
This task is a follow-up task to a first grade task "Valid Equalities?" On the surface, both tasks can be completed with sound procedural fluency in addition and multiplication. However, these tasks present the opportunity to delve much more deeply into equivalence and strategic use of mathematical properties.
Represent and solve problems involving multiplication and division within 100 (Standards 3.OA.1–4 and Standard 3.OA.7)
Students use the four operations to identify and explain patterns in arithmetic (Standards 3.OA.8–9)
The purpose of this task is to study some patterns in a small addition table.
• Making a ten
This task asks students to study more carefully the make-a-ten strategy that they should already know and use intuitively. In this strategy, knowledge of which sums make a ten, together with some of the properties of addition and subtraction, are used to evaluate sums which are larger than 10.
• Patterns in the multiplication table
This task is intended for instruction. The goal is to look for structure and identify patterns and then try to find the mathematical explanation for this. This problem examines the ''checkerboard'' pattern of even and odd numbers in a single digit multiplication table.
• Symmetry of the addition table
The goal of this task is to help students understand the commutative property of addition by examining the addition facts for single digit numbers.
• The Class Trip
The purpose of this instructional task is for students to solve a two-step word problem and represent the unknown quantity with a variable. This task also addresses the concept of scarcity.
• The Stamp Collection
In Grade 3, many students will understand half of 120 to mean the number obtained by dividing 120 by 2. For students who are unfamiliar with this language the task provides a preparation for the later understanding that a fraction of a quantity is that fraction times the quantity. Strand: NUMBER AND OPERATIONS IN BASE TEN (3.NBT)
Use place value understanding and properties of operations to perform multi-digit arithmetic. A range of algorithms may be used (Standards 3.NBT.1–3).
• Carlos and Sara Present Their Solutions
This Teaching Channel video shows two students' responses to mental math and student-led solution. (5 minutes)
• Classroom Supplies
In this task students are asked to decide how to spend \$1,000 on supplies and materials for their classroom; students will have to make choices and be careful not to exceed the budget. Students are asked to decide which supplies will benefit the class the most and will compare their choices with other students' choices.
• How Many Colored Pencils?
The purpose of this task is to support students' reasoning based on place value to multiply a single digit number by a multiple of 10.
• Mental Math
This video and lesson plan will help students use the strategies of decomposing, jumps of ten, and splitting. (6 minutes)
• Rounding to 50 or 500
In this task students are asked questions about rounding to the nearest ten and the nearest hundred.
• 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 Ten and Hundred
The purpose of this task is for students to practice rounding numbers to the nearest ten, connect the rules for rounding with location on the number line, and to introduce the idea of rounding to the nearest 100. Strand: NUMBER AND OPERATIONS - FRACTIONS (3.NF)
Develop understanding of fractions as numbers. Denominators are limited to 2, 3, 4, 6, and 8 in third grade. (3.NF.1-3)
• Closest to 1/2
In this task students are given a number line and a choice of fractions. They must identify which of the choices is closest to 1/2.
• Comparing Fractions
The purpose of this task is for students to compare fractions using common numerators and common denominators and to recognize equivalent fractions. Students need to represent their answers with both symbols and pictures, so that the visual representation can help students make meaning of the more abstract symbolic representations.
• Comparing Fractions Game
The goal of this task is to compare 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.
• Comparing Fractions with a Different Whole
This task is meant to address a common error that students make, namely, that they represent fractions with different wholes when they need to compare them.
• Comparing Fractions with the Same Denominator, Assessment Variation
This task is part of a set of three assessment tasks for 3.NF.3d. This part of the standard is about comparing two fractions with the same numerator or the same denominator by reasoning about their size, and understanding that such comparisons are valid only when the fractions refer to the same whole.
• Comparing Fractions with the Same Numerators, Assessment Variation
This task is part of a set of three assessment tasks for 3.NF.3d. This part of the standard is about comparing two fractions with the same numerator or the same denominator by reasoning about their size, and understanding that such comparisons are valid only when the fractions refer to the same whole.
• Find 1
The purpose of this task is to assess whether students understand fractions as being built from unit fractions and whether they can accurately locate fractions on the number line.
• Find 1 Starting from 5/3, Assessment Variation
This is the third of three summative assessment tasks for 3.NF.2 that progress in difficulty. Each requires that students "understand a fraction as a number on the number line" and "represent fractions on a number line diagram."
• Find 1/4 Starting from 1, Assessment Version
This is the first of three summative assessment tasks for 3.NF.2 that progress in difficulty. Each requires that students "understand a fraction as a number on the number line" and "represent fractions on a number line diagram."
• Find 7/4 starting from 1, Assessment Variation
This is the second of three summative assessment tasks for 3.NF.2 that progress in difficulty. Each requires that students "understand a fraction as a number on the number line" and "represent fractions on a number line diagram."
• Finding 2/3
This simple-looking problem reveals much about how well students understand unit fractions as well as representing fractions on a number line.
• Fraction Comparisons With Pictures, Assessment Variation
This task is part of a set of three assessment tasks for 3.NF.3d. This part of the standard is about comparing two fractions with the same numerator or the same denominator by reasoning about their size, and understanding that such comparisons are valid only when the fractions refer to the same whole.
• Halves, thirds, and sixths
The purpose of this task is for students to use their understanding of area as the number of square units that covers a region, to recognize different ways of representing fractions with area, and to understand why fractions are equivalent in special cases.
• IXL Game: Compare Fractions
This game helps the third grader compare two fractions with the same numerator or the same denominator by reasoning about their size. This is just one of many online games that supports the Utah Math core. Note: The IXL site requires subscription for unlimited use.
• Jon and Charlie's Run
The purpose of this task is to present students with a context where they need to explain why two simple fractions are equivalent and is most appropriate for instruction.
• Locating Fractions Greater than One on the Number Line
Given a number line and a list of fractions, students must mark and label each fraction on the line.
• Locating Fractions Less than One on the Number Line
In every part of this task, students must treat the interval from 0 to 1 as a whole, partition the whole into the appropriate number of equal sized parts, and then locate the fraction(s) on a number line.
• Naming the Whole for a Fraction
The goal of this task is to show that when the whole is not specified, which fraction is being represented is left ambiguous.
• Ordering Fractions
The purpose of this task is to extend students' understanding of fraction comparison and is intended for an instructional setting.
• Snow Day
The purpose of this task is for students to investigate a claim about a comparison of two fractions in a context. This particular task helps students to construct viable arguments and critique the reasoning of others. Students are asked to critique the reasoning of Alec's claim that his school day was shorter than his brother's in the scenario given.
• 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)
• Which is Closer to 1?
In this problem students are given 2 fractions and asked to determine which of them is closest to 1. Strand: MEASUREMENT AND DATA (3.MD)
Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. (3.MD.1–2)
• Dajuana's Homework
The purpose of this task is for students to work on elapsed-time questions. This task includes three different elapsed time situations: end-time unknown, elapsed time unknown, and start-time unknown.
• How Heavy?
In this activity students measure the weight of various objects using a balance scale and cubes and record the results.
Represent and interpret data (Standards 3.MD.3– 4)
• Classroom Supplies
In this task students are asked to decide how to spend \$1,000 on supplies and materials for their classroom; students will have to make choices and be careful not to exceed the budget. Students are asked to decide which supplies will benefit the class the most and will compare their choices with other students' choices.
• Introduction to Bar Graphs
This lesson is designed to have students practice making bar graphs and interpret those graphs.
Understand concepts of area and relate area to multiplication and addition (Standards 3.MD.5–7)
• Finding the Area of Polygons
The purpose of this instructional task is for students to find the area of figures that can be decomposed and then recomposed into rectyangles.
• Fixed Areas
This lesson plan activity helps students understand the relation between area and perimeter.
• Geoboards in the Classroom
This site offers the teacher lesson plans and resources for exploring the area of two-dimensional objects.
• Halves, thirds, and sixths
The purpose of this task is for students to use their understanding of area as the number of square units that covers a region, to recognize different ways of representing fractions with area, and to understand why fractions are equivalent in special cases.
• Introducing the Distributive Property
This is an instructional task, best used when students are first working with the distributive property. The standard asks students to apply the distributive property to area models, though this task intentionally begins with array models.
• Junior Architects
This unit of 4 lessons leads students to design a clubhouse and thereby review two- and three-dimensional shapes, calculate perimeter and area, and create blueprints and three-dimensional models.
• Length, Perimeter, and Area
This lesson will help students understand how to find the area and perimeter of a random shape and a random triangle.
• The Square Counting Shortcut
Students are given 4 pictures made up of squares. This is a rectangle subdivision task; ideally instead of counting each square. students should break the letters into rectangles, multiply to find the areas, and add up the areas.
• Three Hidden Rectangles
The purpose of this task is for students to decompose a figure into rectangles and then find the total area by adding the area of all of its smaller, non-overlapping rectangles. This task also requires students to create expressions to represent the area of the entire figure as the sum of the areas of the rectangles.
Recognize perimeter as an attribute of plane figures and distinguish between linear and area measures (Standard 3.MD.8)
• Fixed Areas
This lesson plan activity helps students understand the relation between area and perimeter.
• Junior Architects
This unit of 4 lessons leads students to design a clubhouse and thereby review two- and three-dimensional shapes, calculate perimeter and area, and create blueprints and three-dimensional models.
• Length, Perimeter, and Area
This lesson will help students understand how to find the area and perimeter of a random shape and a random triangle.
• Perimeter
This lesson plan and activities will help students understand the concept of perimeter.
• Shapes and their Insides
The purpose of this task is to help students differentiate between a polygon and the region inside of a polygon so that they understand what is being measured when the perimeter and area are being found. Strand: GEOMETRY (3.G)
Reason with shapes and their attributes. (Standards 3.G.1–2)
In this lesson the student is introduced to parallelograms, rectangles, and trapezoids and practices creating various types of quadrilaterals.
• Geometric pictures of one half
This task presents students with some creative geometric ways to represent the fraction one half. The goal is both to appeal to students' visual intuition while also providing a hands on activity to decide whether or not two areas are equal. Students should be given paper models of each picture which they can fold or cut and rearrange so as to help visualize why the shaded and unshaded areas are equal.
• Halves, thirds, and sixths
The purpose of this task is for students to use their understanding of area as the number of square units that covers a region, to recognize different ways of representing fractions with area, and to understand why fractions are equivalent in special cases.
• Perimeter
This lesson plan and activities will help students understand the concept of perimeter.
• Representing Half of a Circle
Given a number of pictures of circles with darkened areas, students are asked to decide if half of the circle is shaded. This task is meant for instructional purposes, and students should have access to multiple copies of the figures and be encouraged to experiment by cutting them and comparing the pieces.
• 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)   The Online Core Resource pages are a collaborative project between the Utah State Board of Education and the Utah Education Network. If you would like to recommend a high quality resource, contact Trish French (Elementary) or Lindsey Henderson (Secondary). If you find inaccuracies or broken links contact resources@uen.org.