Forward
Fifth grade is the time to focus on fractions and decimals and their operations in great detail. Students also deepen their understanding of whole numbers, get introduced to the calculator, learn more problem solving and geometry, and study statistical graphs.
The year starts out with a study of whole numbers and their operations. Students review multi-digit multiplication and learn long division with two-digit divisors. We also review divisibility and prime factorization from fourth grade.
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In the second chapter, the focus is on large numbers and using a calculator. This is the first time a done with mental math or with paper and pencil. I want students to learn to be critical in their use of the calculator and use it with good judgment. Every exercise where calculator use is allowed is marked with a little picture of a calculator.
The third chapter is about equations and problem-solving. We study simple equations with the help of a balance and bar models. The main goal is to get students used to the concept of an equation and what it means to solve an equation. Students also solve a fair amount of word problems with the help of the visual bar model.
The fourth chapter is about decimals and some of the operations with decimals (the rest will be studied in chapter 6). Fifth grade is the time when students learn all the basic operations with decimals. In this chapter, we focus on place value with decimals, addition and subtraction of decimals, and multiplication and division of decimals by whole numbers.
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Multiplying decimals by decimals and dividing decimals by decimals is covered in chapter 6.
In chapter 5 we study graphing in a coordinate grid, line and bar graphs, and average and mode.
Today’s world has become increasingly complex with lots of data presented in the media, so our children need a good grasp of statistical graphs to be able to make sense of all of that information.
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Chapter 1: The Four Operations
Chapter 2: Large Numbers and the Calculator
Chapter 3: Problem Solving
Chapter 4: Decimals, Part 1
Chapter 5: Statistics and Graphing
Chapter 6: Decimals, Part 2
Chapter 7: Fractions: Add and Subtract
Chapter 8: Fractions: Multiply and Divide
Chapter 9: Geometry
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The Lessons in Chapter 1
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Warm Up: Mental Math
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The Order of Operations and Equations
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Review: Addition and Subtraction
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Review: Multiplication and Division
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Multiplying in Parts
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The Multiplication Algorithm
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More Multiplication
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Long Division
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A Two-Digit Divisor 1
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A Two-Digit Divisor 2
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Long Division and Repeated Subtraction
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Divisibility Rules
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Review: Factors and Primes
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Prime Factorization
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MENTAL MATH
Math Mahjong
A Mahjong game where you need to match tiles with the same value.
Pop the Balloons
Pop the balloons in the order of their value. You need to use all four operations.
ORDER OF OPERATIONS
Interactive Order of Operations Practice
Click on the correct operation in the expression.
Order of Operations Practice
A simple online quiz of 10 questions. Uses parentheses and the four operations.
The Order of Operations Millionaire
Answer multiple-choice questions that have to do with the order of operations, and win a million.
Exploring the Order of Operations (Object Interactive)
Click on the correct operation to be done first in the given expression. The program then solves that operation, and you click on the next operation to be performed. Lastly the resource includes a game where you click on the falling blocks in the order that the order of operations would dictate.
Choose Math Operation
Choose the mathematical operation(s) that make the equation true. Practice the role of zero and one in basic operations or operations with negative numbers. Helps develop number sense and logical thinking.
Quick Calculate
Practice your arithmetic with all four operations plus the order of operations.
Free worksheets for the order of operations
Generate printable and customizable worksheets for the order of operations. Choose from five operations and parentheses. You can choose the number range used, the number of problems, and more.
BAR MODELS
Thinking Blocks: Addition and Subtraction
Model and solve addition and subtraction word problems using this interactive math tool. This link takes you to the Thinking Blocks main page; scroll down to the section titled Addition and Subtraction.
Thinking Blocks: Multiplication and Division
Model and solve multiplication and division word problems using this interactive tool. The link takes you to the Thinking Blocks main page; scroll down to the section on multiplication and division.
FUN WITH PROBLEM SOLVING
Calculator Chaos
Most of the keys have fallen off the calculator. Make certain numbers using the keys that are left.
SpeedMath Deluxe
Create an equation from the four given digits using addition, subtraction, multiplication and division. Make certain that you remember the order of operations. It sometimes includes negative numbers.
Random Coins
Can you make $1.00 from Random Coins? Drag and drop the coins.
LONG DIVISION & MULTIPLICATION
Amoeba Multiplication Game
Practice partial products, or multiplication by splitting numbers. Choose “Medium Level”.
Area and the Distributive Property
Practice the idea how partial products tie in with the area of a rectangle (the distributive property).
Multiply 2-Digit Numbers with Area Model
Use an area model to decompose factors and multiply.
Estimator Quiz
Practice your estimation skills in this customizable interactive quiz. Choose “multiplication”.
Interactive Multiplication Practice
Improve your multi-digit multiplication skills with this 10-question online quiz.
Multiplication with Money
Spin the wheel. At the end of each spin, practice multiplying amounts of money.
Understanding Remainders
Use arrays and practice problems to understand remainders. Also includes a bonus game!
Drag and Drop Math
An interactive tool to practice long division or long multiplication.
Mr. Martini’s Classroom: Long Division
An interactive long division tool.
Long Division
Solve long division problems interactively. Choose the levels with 2-digit divisors.
Long Division Tic Tac Toe
Play Tic Tac Toe while solving long division problems. This exercise has multiple-choice answers.
Long Division by “Chunking”
Solve division problems by using the “chunking method” — also called division by repeated
subtraction.
Short Division
A page that explains short division in detail. Short division is the same algorithm as long division, but some steps are only done in one’s head, not written down.
FACTORS AND PRIMES
Divisibility Quiz Generator
Generate customized quizzes to practice the rules of divisibility.
Primes and Divisibility Quiz
Practice basic concepts of primes and divisibility with this interactive self-check quiz.
Arrays and factors
Drag rectangles to show the factorizations of a given number on a grid.
Octopus Factors
Move counters up the legs of an octopus but only when the number on the circle is a multiple of the number on the card.
Factor Game
Choose a number from the game board, and your opponent gets all the numbers that are its proper factors. Adjust the number of rows and columns of the board to get a more challenging game. This game can easily be adapted to be played offline, with paper and colored pencils.
Product Game
The players choose factors and the product of those are colored in on the game board. The player who gets four products in a row wins. You can play against the computer or with a friend. This game can easily be adapted to be played offline, with paper and colored pencils.
Prime Factorization Calculator
This tool allows you to enter a composite number, and it produces a list of the prime numbers that, when multiplied, produce the original composite number.
Sliding Tile Factorization Game
Slide a number over another to capture it. You can only do this if the number you slide is a factor of the other. Number 1 is only supposed to be used to capture prime numbers.
Not a Factor
Choose a number that is not a factor of the given number.
Factorization Forest
A fun game where for each number you factorize, you will get to grow a tree in your forest!
Factoring Calculator
This tool lists all the factors of a given number and has an interesting visual that pairs the factors of the number. You can find all the factors of even very large numbers. It's fun to experiment with!
Factor Trees at Math Playground
Factor numbers to their prime factors using an interactive factor tree.
MathGoodies Interactive Factor Tree Game
Type the missing number into the factor tree, and you will see the factor tree being drawn.
FOR FURTHER STUDY
Unique Prime Factorization
A video explaining the fundamental theorem of arithmetic: that each composite number has a unique prime factorization.
Primes, Factors and Divisibility—Explorer at CountOn.org
Explore and learn more about divisibility tests, primes, and factors.
The Prime Pages
Learn about the largest known primes, how primes are found, how many there are, and more.
Primality of 1 from Wikipedia
Discussing whether 1 should or should not be counted as a prime number.
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