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Maths • Geometry & Algebraic Thinking

Geometry and Algebra Quest

Evaluate expressions, graph points on a coordinate plane, and classify two-dimensional shapes using hierarchy.

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Activities

Learning Goals

  • ✓Evaluate expressions using order of operations.
  • ✓Graph ordered pairs in the first quadrant.
  • ✓Explain shape classification using properties.
  • ✓Understand that shape categories can fit inside larger categories.

Mini Lesson

  1. 1Order of operations tells which part of an expression to solve first.
  2. 2Parentheses are solved before multiplication and addition.
  3. 3An ordered pair is written as (x, y). Move right first, then up.
  4. 4Shapes can be classified by properties such as parallel sides, equal sides, and right angles.
  5. 5Some shape categories are inside other categories.
parenthesesexpressionorder of operationscoordinate planeordered pairhierarchyparallelogramrhombussquare

Interactive Activities

Tap an answer choice. The card will show feedback, the correct answer, visual model, and step-by-step explanation.

🚗
Activity 1Order of Operationsquiz

Car Wash Order of Operations

Question

Leo has $15. He washes 2 cars for $12 each, but spends $4 on soap for each car. Evaluate: 15 + (12 - 4) × 2.

Instruction

Use order of operations. Solve inside parentheses first, then multiply, then add.

💡 Teacher Hint

Start with 12 - 4.

👁️ Show Visual Model: Funnel Breakdown
Model Type: funnel-model
15 + (12 - 4) × 2
       └───┬───┘
           ▼
15 +   8   × 2
       └───┬───┘
           ▼
15 +      16
 └────┬────┘
      ▼
     31

Final answer: $31
✅ Show Step-by-Step Answer
  1. 1Start with the expression: 15 + (12 - 4) × 2.
  2. 2Solve inside parentheses: 12 - 4 = 8.
  3. 3The expression becomes 15 + 8 × 2.
  4. 4Multiply before adding: 8 × 2 = 16.
  5. 5Add 15 + 16 = 31.
  6. 6Leo has $31.
CCSS 5.OA.A.1
🛝
Activity 2Coordinate Planecoordinate

Park Map Coordinate

Question

A park map has an ice cream shop at the origin (0,0). To get to the playground, a visitor walks 4 units east and 7 units north. What is the coordinate point of the playground?

Instruction

Move right 4 units on the x-axis, then move up 7 units on the y-axis.

💡 Teacher Hint

East means right. North means up. Ordered pairs are written as (x, y).

Target Coordinate

(4, 7)

👁️ Show Visual Model: Coordinate Grid Trajectory
Model Type: coordinate-grid
Y-Axis
 7 ──┐        Playground: (4, 7)
 6   │
 5   │
 4   │
 3   │
 2   │
 1   │
 0 ──┴────► X-Axis
     1 2 3 4

Start at (0,0).
Move right to 4.
Move up to 7.
Answer: (4, 7)
✅ Show Step-by-Step Answer
  1. 1Start at the origin: (0, 0).
  2. 2Move 4 units east, which means right.
  3. 3The x-coordinate is 4.
  4. 4Move 7 units north, which means up.
  5. 5The y-coordinate is 7.
  6. 6The playground is at (4, 7).
CCSS 5.G.A.1
◼️
Activity 3Classifying 2D Shapesclassification

Shape Classification Map

Question

Samantha states that every square is also a rhombus. Is her statement true or false?

Instruction

Use shape properties. A rhombus has 4 equal sides. A square has 4 equal sides and 4 right angles.

💡 Teacher Hint

A square has all the properties of a rhombus, plus right angles.

👁️ Show Visual Model: Shape Hierarchy Diagram
Model Type: hierarchy-diagram
┌─────────────────────────────────────────────────────────┐
│ Parallelograms: opposite sides are parallel              │
│  ┌───────────────────────────────────────────────────┐  │
│  │ Rhombuses: 4 equal sides                           │  │
│  │  ┌─────────────────────────────────────────────┐  │  │
│  │  │ Squares: 4 equal sides AND 4 right angles    │  │  │
│  │  └─────────────────────────────────────────────┘  │  │
│  └───────────────────────────────────────────────────┘  │
└─────────────────────────────────────────────────────────┘

Squares live inside rhombuses.
Statement: TRUE
✅ Show Step-by-Step Answer
  1. 1A rhombus is a quadrilateral with 4 equal sides.
  2. 2A square has 4 equal sides.
  3. 3A square also has 4 right angles.
  4. 4Because a square has all the properties of a rhombus, it belongs inside the rhombus category.
  5. 5Therefore, every square is a rhombus.
CCSS 5.G.B.3CCSS 5.G.B.4

Exit Ticket

Why is every square a rhombus, but not every rhombus is a square?

Show Suggested Answer

Every square has 4 equal sides, so it is a rhombus. But a rhombus does not always have 4 right angles, so not every rhombus is a square.

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