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). They demonstrate understanding of the properties of multiplication and the relationship between multiplication and division (Standards 3.OA.5–6). 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.
• Analyzing Word Problems Involving Multiplication
The purpose of this task is for students to analyze different contexts in which multiplication is appropriate.
• Arithmetic Four
In this game for two players, students solve problems involving whole number and integer addition, subtraction, multiplication, and division.
• 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.
• Clock Arithmetic
In this activity students experiment with clock arithmetic and use long division skills.
• Discover Number Patterns With Skip Counting
This Teaching Channel video shows students looking for patterns when counting by 200s. (7minutes)
• Factor Trail Game
In this lesson students will practice identifying the integer factors of numbers up to 100.
• 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?"
• Grade 3 Math Module 1: Properties of Multiplication & Division & Solving Problems with Units of 2-5
This 25-day module begins the year by building on students' fluency with addition and knowledge of arrays.
• Grade 3 Math Module 3: Multiplication & Division w/ Units of 0, 1, 6-9, and Multiples of 10
This 25-day module builds directly on students work with multiplication and division in Module 1. Module 3 extends the study of factors from 2, 3, 4, 5, and 10 to include all units from 0 to 10, as well as multiples of 10 within 100. Similar to the organization of Module 1, the introduction of new factors in Module 3 spreads across topics. This allows students to build fluency with facts involving a particular unit before moving on. The factors are sequenced to facilitate systematic instruction with increasingly sophisticated strategies and patterns.
• Grade 3 Mathematics Module 7: Geometry and Measurement Word Problems (EngageNY)
This 40-day final module of the year offers students intensive practice with word problems, as well as hands-on investigation experiences with geometry and perimeter. The module begins with solving one- and two-step word problems based on a variety of topics studied throughout the year, using all four operations. Next students explore geometry. Students tessellate to bridge geometry experience with the study of perimeter. Line plots, familiar from Module 6, help students draw conclusions about perimeter and area measurements. Students solve word problems involving area and perimeter using all four operations. The module concludes with a set of engaging lessons that briefly review the fundamental Grade 3 concepts of fractions, multiplication, and division.
• IXL Game: Complete the addition, subtraction, multiplication, or division sentence
This game helps third graders solve two-step word problems using the four operations. This is just one of many online games that supports the Utah Math core. Note: The IXL site requires subscription for unlimited use.
• 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.
• 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.
• Pascal's Triangle
Students will learn about Pascal's triangle and practice their skills in multiplication and division in this lesson plan.
• 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.
• Planning Full Days & Practicing Fast Facts
In this Teaching Channel video an educator demonstrates how to plan a daily routine and teach multiplication facts. (6 minutes)
• Recognizing Patterns
This lesson will introduce students to patterns in sequences and tessellations and give them practice in creating their own patterns.
• Sample Scope and Sequence
This sample scope and sequence document for the implementation of the new Math core for Grade 3 based on 160 days of instruction - 16 units.
• 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.
• 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?"
• USBE Core Guide for Domain: Operations and Algebraic Thinking (3OA1)
This math guide provides academic vocabulary, instructional strategies, teacher resources, and assessment tasks for the Operations and Algebraic Thinking domain.
• USBE Core Guide for Domain: Operations and Algebraic Thinking (3OA2)
This math guide provides academic vocabulary, instructional strategies, teacher resources, and assessment tasks for the Operations and Algebraic Thinking domain.
• USBE Core Guide for Domain: Operations and Algebraic Thinking (3OA3)
This math guide provides academic vocabulary, instructional strategies, teacher resources, and assessment tasks for the Operations and Algebraic Thinking domain.
• USBE Core Guide for Domain: Operations and Algebraic Thinking (3OA4)
This math guide provides academic vocabulary, instructional strategies, teacher resources, and assessment tasks for the Operations and Algebraic Thinking domain.
• USBE Core Guide for Domain: Operations and Algebraic Thinking (3OA5)
This math guide provides academic vocabulary, instructional strategies, teacher resources, and assessment tasks for the Operations and Algebraic Thinking domain.
• USBE Core Guide for Domain: Operations and Algebraic Thinking (3OA6)
This math guide provides academic vocabulary, instructional strategies, teacher resources, and assessment tasks for the Operations and Algebraic Thinking domain.
• USBE Core Guide for Domain: Operations and Algebraic Thinking (3OA7)
This math guide provides academic vocabulary, instructional strategies, teacher resources, and assessment tasks for the Operations and Algebraic Thinking domain.
• USBE Core Guide for Domain: Operations and Algebraic Thinking (3OA8)
This math guide provides academic vocabulary, instructional strategies, teacher resources, and assessment tasks for the Operations and Algebraic Thinking domain.
• USBE Core Guide for Domain: Operations and Algebraic Thinking (3OA9)
This math guide provides academic vocabulary, instructional strategies, teacher resources, and assessment tasks for the Operations and Algebraic Thinking domain.
• 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.

http://www.uen.org - in partnership with Utah State Board of Education (USBE) and Utah System of Higher Education (USHE).  Send questions or comments to USBE Specialist - Shannon Ference and see the Mathematics - Elementary website. For general questions about Utah's Core Standards contact the Director - DIANA SUDDRETH .
Email:  diana.suddreth@schools.utah.gov

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