Assignment: Problem solving — Chapter 1 - Patterns in Mathematics
In this assignment you will solve problems about "Chapter 1 - Patterns in Mathematics" and show your working clearly.
Learning objectives
- Recognise a pattern in a set of numbers, shapes, or events, and explain why it is a pattern rather than a coincidence.
- Describe, extend, and create number patterns such as triangular numbers, square numbers, cube numbers, the doubling pattern, and the Virahanka (Fibonacci-style) numbers.
- Discover hidden connections between different number patterns, including their appearance inside Pascal's Triangle and their link to the golden ratio.
- Represent a pattern using dots, shapes, grids, tables, or a simple chart.
Instructions
Complete all tasks in order. Use the lessons of this chapter, show your own thinking, and do not copy answers from the textbook.
Tasks
- A. Multiple Choice Questions (1 mark each)
- What is the next term in the sequence 1, 3, 6, 10, ___?
- 12 (b) 14 (c) 15 (d) 16
- 15 (b) 21 (c) 36 (d) 40
- In the doubling pattern 1, 2, 4, 8, 16, what is the 7th term?
- Calculate: 1 × 1
- Make up one word problem of your own about Introduction: The World Runs on Patterns, then solve it.
- For every problem, write each step of your working and check your answer.
Submission requirements
- Format: neat handwritten working (photo or scan) or typed working, with each problem numbered.
- Length: about one to two pages (200–300 words of writing).
- Submit online in this assignment as text and/or uploaded files before the due date.
Marks and assessment criteria
This assignment is marked out of 20 using the rubric below.
| Criterion | Levels (marks) | Maximum |
|---|---|---|
| Method and working | Excellent: correct method with every step shown (8) | Good: correct method with most steps shown (6) | Satisfactory: partly correct method or steps missing (3) | Needs improvement: no working or an incorrect method (0) | 8 |
| Accuracy of answers | Excellent: all answers correct with units (6) | Good: most answers correct (4) | Satisfactory: some answers correct (2) | Needs improvement: few or no correct answers (0) | 6 |
| Understanding of the problem | Excellent: identifies all given information and what is asked (4) | Good: identifies most of the information (3) | Satisfactory: identifies some information (2) | Needs improvement: does not show what is given or asked (0) | 4 |
| Presentation | Excellent: neat, well organised and complete (2) | Satisfactory: readable but disorganised in places (1) | Needs improvement: hard to follow or incomplete (0) | 2 |
| Total | 20 |
Teachers can edit these instructions, the submission settings, the due date and the rubric in the assignment settings.
Chapter 1 - Patterns in Mathematics: Assignment Extra Practice
To develop pattern recognition skills by identifying, extending, creating, and analyzing repeating, growing, and visual patterns in numbers, shapes, and real-life contexts, and to understand how rules govern predictable arrangements.
Instructions
- Complete all tasks on paper or in your notebook.
- Show your work and explain your reasoning for each task.
- Use diagrams, grids, or sketches where helpful.
- Submit your completed work by the due date.
Tasks
- Task 1 - Pattern Hunt: Look around your home or classroom for 5 minutes. Sketch and describe two different patterns you see (e.g., floor tiles, window grilles, book arrangements). For each, identify the pattern type (repeating, growing, shrinking, or visual) and state the rule in your own words.
- Task 2 - Number Pattern Extension: Write the next three terms and the rule for each sequence: (a) 7, 14, 21, 28, ___ (b) 50, 45, 40, 35, ___ (c) 1, 3, 6, 10, 15, ___ (d) 1, 4, 9, 16, 25, ___. Name the pattern family for each (skip-counting, shrinking, triangular numbers, square numbers).
- Task 3 - Grid Investigation: Draw a 5×5 number grid (numbers 1–25). Shade all multiples of 4. Describe the pattern you see. Does it form diagonal stripes like the multiples of 3 on a 10×10 grid? Explain why or why not, referring to the grid width and the multiple.
- Task 4 - Visual Pattern Construction: Using dots, draw the first five triangular numbers and the first five square numbers. For the square numbers, also draw the gnomon (L-shaped layer) added at each step. List the number of dots in each gnomon and describe the pattern you notice in the gnomon sizes.
- Task 5 - Rule Discovery: A pattern starts with 2 dots. Each new term adds a row of dots with 2 more dots than the previous row (first row: 2, second row: 4, third row: 6, ...). Draw the first four terms. Find the total dots in each term. Write a rule for the total dots in term n. Predict the total for term 10 without drawing.
- Task 6 - Connection Challenge: Verify that adding two consecutive triangular numbers gives a square number. Test this for the first four pairs (1+3, 3+6, 6+10, 10+15). Then explain in your own words why this relationship might always hold true, using a diagram or description of dot arrangements.
Submission checklist
- Sketches and descriptions for Task 1 (two real-life patterns with rules).
- Completed sequences, rules, and pattern family names for Task 2.
- 5×5 grid with multiples of 4 shaded and written explanation for Task 3.
- Dot drawings for triangular numbers, square numbers, and gnomons with gnomon size list for Task 4.
- Drawings, totals, rule, and prediction for Task 5.
- Verification calculations and explanation for Task 6.
Reflect on your learning
- How does using a grid or visual diagram help you see patterns that are not obvious in a simple list of numbers? Give an example from this assignment.
- Think of a situation outside of math class (sports, music, nature, daily routine) where recognizing a pattern and its rule helps you predict what will happen next. Describe the pattern, its rule, and why prediction is useful there.
Completion requirements:
- Make a submission