Algebra Games for 5th Graders

Why is Algebraic Thinking Important?

1. Algebraic thinking provides the foundation for children to move beyond the specific computational skills to the general manipulation of algebra symbols.  For example:

2. Algebraic thinking is to explore, observe, predict and understand patterns.

a. Repeating and growing patterns can be found in numbers. For example:

1, 2, 1, 2, ___, ___, ___

1, 3, 5, 9, ___, ___, ___

1, 3, 6, 10, 15, 21, ___, ___, ___

b. Patterns are a vehicle that enables children to make sense of the world around them.

Examples: Rhythmic patterns, seasons, phases of the moon

c. Using patterns to solve algebra problems is an extremely powerful tool for making connections in mathematics. Examples:

Doubles: 2 + 2 = 4

Doubles Plus One: 2 + 3 = 5

Skip Counting 3, 6, 9, 12, 15, 18, ...

Function Machines

3. Algebraic thinking is fundamental to functioning in business, industry, science, technology and daily life.

Algebra Games and Activities for 5th Graders

Math games and problem-solving activities are essential for children to enjoy and explore the subject. Educational games provide repetitive practice and multiple approaches to solve math problems. Fun math activities for kids are also very engaging. Constructing the design using manipulatives and math aids is critical for several reasons. Students link patterns to spatial thinking and algebraic geometry. Visual representations help to develop abstract thinking. Furthermore, students require a concrete representation in order to make sense of the pattern Following are some math activities to learn basic algebra and abstract algebra in an entertaining and engaging way in 5th grade math:

GROWING WEAVE DESIGNS ACTIVITY

In this mathematics activity, children investigate the pre algebra concept of growing patterns by modeling the growth of a design, using algebra tiles or interlocking cubes. They represent growth with concrete materials and they generate patterns (such as 4, 8, 12, 16, … and 1, 4, 9, 16, 25, …)

They record patterns and generalize pattern rules using words to describe relationships. They represent the patterns in different ways, using tables, diagrams, graphs, and manipulatives. Provide children with different colored papers and let them weave them to create different designs. Children should be able to recognize and represent the math found within their weave designs. This will help children in writing algebraic expressions to represent the designs created and then solving algebraic expressions for values of the variables. Prior to this learning activity, students should have had some experience with representing patterns using charts, diagrams, graphs, and concrete materials.

We can show the growth pattern by using tiles of two different colors. In the first image, a blue tile represents the design at its starting point. In the second image, black tiles show the growth of the design that has resulted. In the third image, the black tiles are now surrounded by blue tiles, representing the next growth stage. The pattern alternates, with each color surrounding the shape in turn. When modeling the pattern with tiles, you do not need to start over again to show each growth stage – just continue building the previous stage.

The weave design grows in a number of interesting ways:

• The pattern generated by the number of blue color tiles is 1, 1, 9, 9, 25, 25, … . This is a repeating and growing pattern that can be made by squaring the odd numbers and repeating each term twice.

• The black color tiles pattern is represented by the squares of even numbers.

• The additional tiles needed to complete each stage are represented by the multiples of 4 (4, 8, 12, …).

• Counting tiles in the rows (or columns) gives the pattern 1 + 3 + 1 for stage 2, 1 + 3 + 5 + 3 + 1 for stage 3, and so on.

• The rule for successive stages is: stage number squared plus (stage number minus 1) squared will give the total number of tiles.

Let students explore the activity more by asking algebra questions like:

• How might you describe the pattern to someone who can’t see it?

• How many tiles of each color are you adding?

• Predict how many tiles you’ll need for stage 4.

• Did you notice how much the total number of tiles increases from stage to stage?

• Do you think you have enough tiles to complete stage 7?

Children might look at the overall pattern as the number of tiles increases. Encourage children to find the difference between the totals in order to discover the number of tiles added each time. When recording the differences, they may also notice that the pattern increases by multiples of 4 (4 is added first, then 8, then 12 then 16, and so on).

This is the design completed to the end of stage 7:

There are 49 blue tiles and 36 black tiles for a total of 85 tiles. Some students may notice that there are 7 blue tiles along one edge and that this is the 7th stage, for a total of 7 X 7 or 49 blue tiles.

Some kids may need to use algebra calculator to help them discover patterns such as the difference or sum of different colors of tiles. Some students may complete the growth sequence but not identify the pattern of colored tiles. They would benefit from deconstructing the pattern and assembling the tiles into arrays.

Extension to this activity can be to ask kids to use the rule they have discovered to find out the number of tiles in stage 20 without having to extend the chart or using the manipulatives. Solving this new problem will help to deepen their understanding of the pattern.

A variation on the design growth pattern activity is to provide kids with tiles of a third color and ask them to add tiles in this color to the existing weave patterns to create squares. Ask them to model the first three stages, just as they did in the original design growth activity. They should record their results in a table and then look for patterns and develop algebra rules for sequences.

Algebra worksheets asking exploratory questions or plotting graphs for all stages of each color can be provided along with this learning activity to provide more algebra practice problems to kids. For example:

BALANCING ACT ACTIVITY

In this learning activity, kids explore the concept of equality and variables. In the context of a literature connection, students use symbols and letters to represent the masses of different animals and to investigate relationships and express them algebraically. Students identify relationships between the masses of the animals and write math equations that represent balanced tug-of-war teams. Solving algebraic equations is also achieved through this activity.

Prior to this learning activity, children should have had some experience in using variables (symbols or letters) in algebraic expressions, and in modeling with concrete materials.

Ask kids to brainstorm ways they could represent each animal without having to draw each animal. They may suggest using letters, shapes, or graphics.

Their responses may include:

Next, pose the problem for children:

How many different ways can the animals combine on either side of the teeter totter to make the teeter totter balance if you have a fox, 4 turtles, and 6 squirrels?

Deeper learning can be achieved by doing pre algebra worksheets, algebra word problems, and most importantly by asking exploratory questions throughout the activity

Following are the different ways in which children can present their thoughts on this activity

Help kids understand it by rearranging the animals. Write the following equation on the board.

We know this equation is true because we are given that F= T + T + T + T.  Adding a squirrel (S) to both sides maintains the balance. Now rearrange the letters on each side of the equation, as follows:

Ask kids to consider whether the new algebra equations are true. Let them rearrange the letters to create other equations. Once they are comfortable with rearranging animals and letters, let them balance equations with numbers. This will help translating algebraic expressions from symbols to numbers. Write the number 14 on a sheet and then ask: “What numbers could I add to get 14?”

Draw a balance scale on the paper and write 1 + 13 on one side. Then ask, “What could I put on the other side to create a balance?”

Encourage them to see various possibilities to solve the equation and also that they can use more than two addends (e.g., 1+ 3+ 10) and that they can use multiplication, division, or subtraction to create an infinite number of possibilities. Post this activity children should be able to identify the unknown variables or quantities: