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). Gain familiarity with factors and multiples (Standard 4.OA.4). Generate and analyze numeric and shape patterns (Standard 4.OA.5).
• An Introduction to Arithmetic and Geometric Sequences
This lesson plan introduces arithmetic and geometric sequences to students so that they know the terminology and can vary a sequence.
• 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 Growth, Variation 1
This problem states "There are two snakes at the zoo, Jewel and Clyde. Jewel was six feet and Clyde was eight feet. A year later Jewel was eight feet and Clyde was 10 feet. Which one grew more?" The purpose of this task is to foster a classroom discussion that will highlight the difference between multiplicative and additive reasoning.
• Comparing Growth, Variation 2
A scenario and two arguments about it are given. Students are asked to compare the arguments to assess their understanding of multiplicative and additive reasoning.
• 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.
• Doubles Plus One
In this task students are given a table of numbers and are asked to multiply each one by 2 and add 1 and then record their answers. They then are instructed to find patterns in the answers with questions like "Does an odd number multiplied by 2 result in an even or odd number? Why do you think this is?"
• Factor Trail Game
In this lesson students will practice identifying the integer factors of numbers up to 100.
• Factors
This lesson is designed to help students understand factors of whole numbers.
• Finding Factors
This lesson plan's activities give students practice in finding the factors of whole numbers.
• Finding Remainders in Pascal's Triangle
This lesson is designed to reinforce division by using clock arithmetic to find remainders and then find patterns in Pascal's triangle by coloring the remainders in colors.
• Flake Maker
This activity allow students to create custom line deformation fractals and practice skills with pattern recognition and plane geometry.
• Floor Tiles
This lesson will help students identify and examine symmetry in geometric figures as well as describe and classify polygons.
• Grade 4 Mathematics Module 1: Place Value, Rounding, and Algorithms for Addition and Subtraction
In this 25-day module of Grade 4, students extend their work with whole numbers. They begin with large numbers using familiar units (hundreds and thousands) and develop their understanding of millions by building knowledge of the pattern of times ten in the base ten system on the place value chart (4.NBT.1). They recognize that each sequence of three digits is read as hundreds, tens, and ones followed by the naming of the corresponding base thousand unit (thousand, million, billion).
• Grade 4 Mathematics Module 3: Multi-Digit Multiplication and Division
In this 43-day module, students use place value understanding and visual representations to solve multiplication and division problems with multi-digit numbers. As a key area of focus for Grade 4, this module moves slowly but comprehensively to develop students' ability to reason about the methods and models chosen to solve problems with multi-digit factors and dividends.
• Grade 4 Mathematics Module 5: Fraction Equivalence, Ordering, and Operations
In this 40-day module, students build on their Grade 3 work with unit fractions as they explore fraction equivalence and extend this understanding to mixed numbers. This leads to the comparison of fractions and mixed numbers and the representation of both in a variety of models. Benchmark fractions play an important part in students ability to generalize and reason about relative fraction and mixed number sizes. Students then have the opportunity to apply what they know to be true for whole number operations to the new concepts of fraction and mixed number operations.
• Grade 4 Mathematics Module 7: Exploring Measurement with Multiplication
In this 20-day module, students build their competencies in measurement as they relate multiplication to the conversion of measurement units. Throughout the module, students will explore multiple strategies for solving measurement problems involving unit conversion.
• IXL Game: Mixed operations: Addition, subtraction, multiplication, and division word problems
This games helps third graders understand mixed operations: Addition, subtraction, multiplication, and division word problems. This is just one of many online games that supports the Utah Math core. Note: The IXL site requires subscription for unlimited use.
• 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.
• 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.
• 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).
• 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.
• Order of Operations Four
This applet pits two players against each other in solving expressions using the four basic operations.
• Pascal's Triangle
Students will learn about Pascal's triangle and practice their skills in multiplication and division in this lesson plan.
• Patterns in Pascal's Triangle
This lesson plan was designed to help students understand Pascal's Triangle and its patterns.
• 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 4 based on 160 days of instruction - 14 units.
• Sets and the Venn Diagram
This lesson is designed to help students understand the ideas surrounding sets and Venn diagrams.
• Spy Game
Encrypted spy messages are the starting point for this lesson plan on modular arithmetic.
• Tessellate!
This lesson and activity will help the student understand how to classify two-dimensional figures based on properties. The student manipulates shapes to create now polygons.
• 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.
• USBE Core Guide (4NBT5)
This core guide was developed by USBE and Utah educators.
• USBE Core Guide (4OA1)
This core guide was developed by USBE and Utah educators.
• USBE Core Guide (4OA2)
This core guide was developed by USBE and Utah educators.
• USBE Core Guide (4OA3)
This core guide was developed by USBE and Utah educators.
• USBE Core Guide (4OA4)
This core guide was developed by USBE and Utah educators.
• USBE Core Guide (4OA5)
This core guide was developed by USBE and Utah educators.
• Venn Diagrams
This is an interactive lesson in which students must place a number into the correct area of a Venn diagram.

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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