 Mathematics Grade 4

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).
• 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.
• 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.
• 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.
In order to assist educators with the implementation of the Common Core, the New York State Education Department provides curricular modules in Pre-K-Grade 12 English Language Arts and Mathematics that schools and districts can adopt or adapt for local purposes.
• 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.
• Grade 4 Unit 1: Whole Numbers, Place Value, and Rounding (Georgia Standards)
In this unit students will read numbers correctly through the millions, write numbers correctly through millions in standard form, write numbers correctly through millions in expanded form, identify the place value name for multi-digit whole numbers, identify the place value locations for multi-digit whole numbers, round multi-digit whole numbers to any place, fluently solve multi-digit addition and subtraction problems using the standard algorithm and solve multi-step problems using the four operations
• Grade 4 Unit 2: Multiplication and Division of Whole Numbers (Georgia Standards)
In this unit students will solve multi-step problems using the four operations, use estimation to solve multiplication and division problems, find factors and multiples, identify prime and composite numbers and generate patterns.
• 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.
• 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.
• 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.
• Operations and Algebraic Thinking (4.OA) - Fourth Grade Core Guide
The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for Fourth Grade Mathematics - Operations and Algebraic Thinking (4.OA)
• Order of Operations Four
This applet pits two players against each other in solving expressions using the four basic operations.
• The Locker Game
The purpose of this instructional task is for students to deepen their understanding of factors and multiples of whole numbers.
• 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. 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 Specialists - Trish  French or Molly  Basham and see the Mathematics - Elementary website. For general questions about Utah's Core Standards contact the Director - Jennifer  Throndsen.

These materials have been produced by and for the teachers of the State of Utah. Copies of these materials may be freely reproduced for teacher and classroom use. When distributing these materials, credit should be given to Utah State Board of Education. These materials may not be published, in whole or part, or in any other format, without the written permission of the Utah State Board of Education, 250 East 500 South, PO Box 144200, Salt Lake City, Utah 84114-4200.