Math activity
Algebra Adventures: Patterns and Variables
Build a pattern with red and blue blocks — red, blue, red, blue! What comes next? Find patterns on shirts, tiles, and bricks too.
Materials and setup
- colored blocks
- paper
- pencil
- graph paper
- hundred chart
How this changes by age
Pre-K (ages 3–4)
Build a pattern with red and blue blocks — red, blue, red, blue! What comes next? Find patterns on shirts, tiles, and bricks too.
Steps
- Build an AB pattern with two colors of blocks: red, blue, red, blue. What comes next?
- Build an ABC pattern: circle, square, triangle, circle, square, triangle. Extend it 3 more times.
- Find patterns around the house: stripes on a shirt, tiles on the floor, bricks on a wall.
- Create your own pattern using stickers or stamps.
- Fix a 'broken' pattern: remove one piece and have your child find what's missing.
- Tell a grown-up one thing that surprised you.
Learning objectives
- Recognize, create, and extend simple repeating patterns
- Identify patterns in the environment
- Determine missing elements in a pattern sequence
Kindergarten (ages 5–6)
Explore growing patterns and number patterns. Use a balance to understand that both sides of an equation must be equal.
Steps
- Create a growing pattern: 1 block, 2 blocks, 3 blocks. How many come next?
- Find number patterns: count by 2s on a hundred chart and color those numbers. What pattern do you see?
- Use a balance or hanger: put 5 cubes on one side. How many do you need on the other side to balance?
- Solve 'mystery number' problems: 3 + ? = 7. Use cubes to figure out the missing number.
- Create 3 of your own patterns and challenge a family member to extend them.
- Tell a grown-up one thing that surprised you.
Learning objectives
- Identify and extend growing number patterns
- Understand equality using a balance model
- Solve for missing numbers in simple equations
Early elementary (ages 6–8)
Introduce variables and expressions. Solve simple one-step equations, create function tables, and describe pattern rules in words and numbers.
Steps
- Introduce the variable: 'n' stands for a mystery number. If n + 5 = 12, what is n?
- Solve 8 one-step equations with missing values: n + 7 = 15, 24 - n = 16, n x 3 = 21.
- Complete 3 function tables: given the rule (like 'add 4' or 'multiply by 3'), fill in input/output pairs.
- Look at a number sequence (2, 5, 8, 11, ...) and describe the rule in words. Predict the 10th term.
- Write an expression for a real situation: 'You have d dollars and earn $5 more. How much now?' (d + 5).
- Create a function machine: choose a rule, give inputs to a partner, they guess the rule from the outputs.
- In one sentence, tell a parent or sibling what surprised you today.
Learning objectives
- Understand variables as representing unknown values
- Solve one-step equations using inverse operations
- Identify and describe rules for number patterns and function tables
Upper elementary (ages 8–10)
Explore pre-algebra concepts: write and evaluate expressions with variables, solve two-step equations, graph linear patterns, and understand the coordinate plane.
Steps
- Write algebraic expressions for 5 word descriptions: 'six more than a number' = n + 6.
- Evaluate 5 expressions when given the value of the variable: if x = 4, what is 3x + 7?
- Solve 8 two-step equations: 2n + 3 = 15, 4n - 5 = 19.
- Create a function table for the rule y = 2x + 1. Plot the ordered pairs on a coordinate plane. What shape does it make?
- Write an equation for a real-world pattern: a pool fills 3 inches per hour starting from 2 inches. Equation: h = 3t + 2. Graph it.
- Challenge: given a graph showing a linear pattern, write the equation that describes it.
- In one sentence, tell a parent or sibling what surprised you today.
Learning objectives
- Write and evaluate algebraic expressions with variables
- Solve two-step equations
- Graph linear relationships on a coordinate plane
Safety and evidence note
Read the full activity before beginning. An adult should supervise tools, heat, food, outdoor work, movement, and experiments as appropriate. Completion records that the activity was done; the child’s explanation, work sample, photo, or demonstration is stronger evidence of learning than a completion check alone.
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