4th Grade Math: Algebra Games

Number Patterns

Fill in the Correct Number Using Additive Patterns

Fill in the correct number using additive patterns.

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Number Patterns

Fill in the Correct Number Using Subtractive Patterns

Children must fill in the correct number using subtractive patterns.

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Number Patterns

Fill in the Correct Number Using Multiplicative Patterns

Fill in the correct number using multiplicative patterns to make learning fun.

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Number Patterns

Identify the Correct Pattern

Enter the madness of math-multiverse by exploring how to identify the correct pattern.

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Factors And Multiples Skills

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Factors And Multiples

Choose the Correct Multiple

Unearth the wisdom of mathematics by learning how to choose the correct multiple.

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Factors And Multiples

Fill in the Missing Multiples

Sharpen your math skills by filling in the missing multiples.

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Factors And Multiples

Choose Whether True or False

Use your algebra skills to choose between true or false.

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Factors And Multiples

Select the First FIve Multiples of Various Numbers

Have your own math-themed party by learning to select the first five multiples of various numbers.

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Prime And Composite Numbers Skills

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Prime And Composite Numbers

Choose the Prime Number Out of the Given Numbers

Kids must choose the prime number out of the given numbers to practice algebra.

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Prime And Composite Numbers

Identify the Number Which is Not a Prime

Have your own math-themed party by learning to identify the number which is not a prime.

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Prime And Composite Numbers

Identify the Type of Number

Enjoy the marvel of mathematics by exploring how to identify types of numbers.

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Prime And Composite Numbers

Identify the Prime Numbers

Practice the superpower of algebra by learning how to identify prime numbers.

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All Algebra Skills

Number Patterns

Fill in Numbers According to the Number Pattern

Use your algebra skills to fill in numbers according to the number pattern.

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Factors And Multiples

Identify If True or False

Identify if the given statement is true or false.

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Prime And Composite Numbers

Select All the Prime Numbers

Shine bright in the math world by learning how to select all the prime numbers.

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Number Patterns

Identify the Correct Rule of Pattern Used

Dive deep into the world of algebra by learning to identify the correct rule of pattern used.

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Factors And Multiples

Complete Factor Pairs for a Number

Use your algebra skills to complete factor pairs for a number.

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Number Patterns

Identify the Pattern and Fill the Correct Number

Enjoy the marvel of mathematics by learning to identify the pattern to fill the correct number.

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Factors And Multiples

Fill in the Missing Factors

Treat yourself to an immersive learning experience by filling in the missing factors.

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Number Patterns

Recognize the Pattern in the Number Sequence

Use your math skills to recognize the pattern in the number sequence.

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Number Patterns

Recognize the Correct Pattern and Fill Accordingly

Unearth the wisdom of mathematics by learning to recognize the correct pattern and fill accordingly.

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Number Patterns

Generate Patterns from the Rule

Kids must generate patterns from the rule to practice algebra.

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Number Patterns

Generate Patterns (Addition)

Enjoy the marvel of mathematics by exploring how to generate patterns using addition.

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Number Patterns

Generate Patterns (Multiplication)

Take a look at how to generate patterns using the concept of multiplication with this game.

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Number Patterns

Relationship Between Two Patterns

Take a look at the relationship between two patterns with this game.

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Why Is Algebra Important?

Algebra is sometimes referred to as generalized arithmetic because it formalizes arithmetic relationships. Its power lies in the ways it allows us to represent relationships among quantities, to describe properties of operations (such as commutative and distributive), and to describe patterns. Basic algebra rules provide for manipulating symbols, such as simplifying and translating algebraic expressions and then solving for an unknown. Reasoning algebraically is essential to the study of other domains of mathematics, including algebraic geometry, measurement, probability, and data analyses. The algebraic reasoning is also needed in the sciences, the social sciences, and the arts. Earlier, algebra instruction was reserved for older students and focused primarily on the manipulation of algebra symbols and the solutions to basic algebra problems, but today, realizing its significance, elementary algebra is introduced to younger kids with more focus on the "big ideas" of algebra and on reasoning algebraically.

Big Ideas of Algebra

There are three big ideas of algebra to tackle. Although these big ideas of abstract algebra are explained individually, they often appear in simple algebra problems in combination.

Big Idea 1: Variables

A variable can be an object, a geometric shape, or a letter that represents a number of things. Variables are used in three ways- to represent unknowns, to represent quantities that vary, and to generalize properties.

Representing Unknowns

Unknowns are variables that don't vary! That is, they have fixed values. Variables with fixed values are used extensively in equations in the early grades, for example,3 + 2 = n and t + 3 = 7. Kids learn that the same letters or shapes in equations represent the same values.

Following is a fun activity for kids to demonstrate the same:

Children are shown two pictures. In one picture, there are two identical toy cars with a price tag of $2 for both toys. The second picture shows the same toy car and a toy dog with a price tag of$5 for both toys. This problem is their introduction to solving algebraic equations with two unknowns; the two equations are car + car = $2 and car + dog = $5. The unknowns are the price of the toy car and the price of the toy dog. Children will learn in grade 5 how to solve algebra word problems that involve first writing algebraic expressions to represent the mathematical relationships and then solving algebraic expressions for the values of the variables.

Representing Quantities That Vary

In some types of algebra equations, the variables are not fixed. The variables can assume different values. Children can be introduced to the concept of variables as 'representing varying quantities as early as the preschool level and then how to solve algebra problems in later years.

One of the best math aids to illustrate this is the following math activity:

Children are presented with two cups (call them a and b) and 10 chips. Then they are asked to find all different ways in which they can place the chips into the cups. This problem can be represented algebraically by writing a + b = 10. A and b vary because they can have lots of different values. For example, if a = 0, then b = 10; if a = 1, then b = 9; if a = 2, then b = 8; and so on. Not only do children learn that there are 11 different pairs of values that solve the equation, but they also learn that once they choose a value for a, the value of b is determined. Similarly, if they select a value for b, then the value of a is determined.

Variables that take on different values are found in all algebra formulas. Consider the formula for the perimeter of a square. In the formula p = 4s, where s is the side of the square. Now the value of s may be different for different squares.

Generalizing Properties

Children are introduced to special relationships that exist among sets of numbers under specific operations. Children are expected to learn these facts so that the computations are simplified.

If students learn that 3 + 4 = 7, then they also know that 4 + 3 = 7, because for the addition of whole numbers, when you change the order of the addends, the sum remains the same. This rule, the commutative property of addition of whole numbers, holds true for all pairs of whole numbers, so it can be represented using variables as a + b = b + a.

Using variables provides a shorthand way of describing relationships that apply to all numbers in a set.

Big Idea 2: Patterns, Relations, and Functions

Children should investigate numerical and geometric patterns and express them mathematically in words or symbols. They should analyze the structure of the pattern and how it grows or changes, organize this information systematically, and use their analysis to develop generalizations about the mathematical relationships in the pattern.

There are two different types of patterns: those that repeat and those that grow or shrink. A repeating pattern is one in which a group of elements repeats whereas a growing or shrinking pattern is one in which elements don't repeat. Rather, there is a change between successive elements, and every element in the pattern is related to the preceding element in the pattern in the same way.

An example of a growing pattern is 1,3,5,7,9, … each element in the pattern is two more than the preceding element.

An example of a shrinking pattern is 100, 90, 80, 70, ... Each element in the pattern is 10 less than the preceding element. Growing and shrinking patterns lead to generalizations and to then representation of the generalizations using variables. Children learn to describe growing and shrinking patterns in words and to predict what comes next.

The same can be taught through a fun activity for kids. Show them the following image:

Children should be encouraged to explain these patterns verbally and to make predictions about what will happen if the sequence is continued.

Fun math activities for kids like these give opportunity to engage them in thinking about how to articulate and express a generalization—"how can we talk about how this pattern works for a square of any size?" grade 4 kids should be able to predict the next element in a sequence by examining a specific set of examples. By the end of fifth grade, students should be able to generalize by reasoning about the structure of the pattern.

In intermediate algebra, kids can also investigate properties like commutativity, associativity, and distributivity of multiplication over addition. Is 3x5 the same as 5x3? Area model can help children discover these questions. For example:

Another example is to find out if 8x14 can be decomposed into 8x10 + 8x4

Another mathematics activity that can be done with kids is to show the child a pattern of constructions made from cubes like this:

In this math problem, the pattern in figure 1 shows one cube on top and one cube at the bottom, figure 2 shows one cube on top and two cubes at the bottom, figure 3 shows one cube on top and three cubes at the bottom, and so on. The child might describe the pattern by saying, "the number of cubes on the bottom is the same as the number of the figure. There is always one cube on top."

Children can use symbols to write the function that shows the relationship between the total number of cubes (let's call it t) and the figure number (let's call it n). The function would be t = n + 1.

Children also identify patterns when they complete function tables. They learn that for every input there is exactly one output. In pre algebra, kids complete function tables when the rule is given, such as "add 3." but in later grades, they not only complete function tables when the rule is given, but they also have to collect data, organize the data in a table, figure out the function, and record the function using symbols.

Big Idea 3: Proportions and Proportional Reasoning

A proportion is a special type of function in which the relationship between quantities is multiplicative. Reasoning about quantities that are related by multiplication is referred to as proportional reasoning. Proportional reasoning is encountered by kids in early years. For example, in the study of place value, students learn that 1 ten is equal to 10 ones, so they figure that 2 tens (2 x 10) is equal to 20 ones, 3 tens (3 x 10) is equal to 30 ones-each regrouping involves multiplication.

In the study of measurement, when children know that there are 4 cups in 1 quart, they can reason that there must be 8 cups (2 x 4) in 2 quarts, and 12 cups (3 x 4) in 3 quarts. In this process, the child is reasoning proportionally. When students construct equivalent fractions and when they use the key on a map to figure out actual distances between cities, they are reasoning proportionally.

Algebraic Thinking in Grade 4

In grade 4, basic algebraic ideas should emerge and be investigated because children—

Identify or build numerical and geometric patterns;
Describe patterns verbally and represent them with tables or symbols;
Look for and apply relationships between varying quantities to make predictions;
Make and explain generalizations that seem to always work situations;
Use graphs to describe patterns and make predictions;
Explore number properties;
Use invented notation, standard symbols, and variables to express a pattern, generalization, or situation.

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4th Grade Math: Algebra Games

Number Patterns Skills

Fill in the Correct Number Using Additive Patterns

Fill in the Correct Number Using Subtractive Patterns

Fill in the Correct Number Using Multiplicative Patterns

Identify the Correct Pattern

Factors And Multiples Skills

Choose the Correct Multiple

Fill in the Missing Multiples

Choose Whether True or False

Select the First FIve Multiples of Various Numbers

Prime And Composite Numbers Skills

Choose the Prime Number Out of the Given Numbers

Identify the Number Which is Not a Prime

Identify the Type of Number

Identify the Prime Numbers

All Algebra Skills

Fill in Numbers According to the Number Pattern

Identify If True or False

Select All the Prime Numbers

Identify the Correct Rule of Pattern Used

Complete Factor Pairs for a Number

Identify the Pattern and Fill the Correct Number

Fill in the Missing Factors

Recognize the Pattern in the Number Sequence

Recognize the Correct Pattern and Fill Accordingly

Generate Patterns from the Rule

Generate Patterns (Addition)

Generate Patterns (Multiplication)

Relationship Between Two Patterns