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 - Grade 6 Assignment Extra Practice
To develop pattern recognition skills by identifying, describing, extending, and creating patterns using numbers, shapes, and grids, and to understand how rules govern predictable arrangements in mathematics and daily life.
Instructions
- Complete all tasks in order. Show your work clearly.
- Use only materials available at home or school (paper, pencil, ruler, coloured pencils).
- For grid tasks, draw your own grids on paper.
- Write rules in clear words and, where helpful, as simple expressions.
- Submit your completed work as a single packet with this checklist on top.
Tasks
- Pattern Hunt: Walk around your home or classroom for 5 minutes. Sketch two different patterns you see (e.g., floor tiles, window grilles, fabric prints, book arrangements). For each, write the rule that makes it a pattern (repeating, growing, shrinking, or visual).
- Number Sequence Detective: For each sequence below, write the next three terms and state the rule in words. a) 7, 14, 21, 28, ___ , ___ , ___ b) 50, 45, 40, 35, ___ , ___ , ___ c) 2, 4, 8, 16, ___ , ___ , ___ d) 1, 1, 2, 3, 5, 8, ___ , ___ , ___ (Hint: each term comes from the two before it.)
- Grid Investigation: Draw a 10×10 grid numbered 1 to 100. Shade all multiples of 4. Describe the pattern you see. Does it form diagonal stripes like the multiples of 3? Explain why or why not using the idea of grid width and step size.
- Build Triangular and Square Numbers: Using dots (draw them), construct the first 5 triangular numbers and the first 5 square numbers. Label each figure with its term number and total dots. Then: a) Write the rule for getting the next triangular number. b) Write the rule for getting the next square number using the gnomon (L-shaped layer) method. c) Verify that adding two consecutive triangular numbers gives a square number (show two examples).
- Skip-Counting Comparison: On the same axes, plot the first 10 terms of skip-counting by 2, by 3, and by 5 (term number on horizontal axis, value on vertical axis). Use different colours. Write one sentence comparing the steepness of the three patterns and what it tells you about growth rate.
- Real-World Prediction: A school assembly seats students in rows. Row 1 has 10 seats, Row 2 has 12 seats, Row 3 has 14 seats, and so on, adding 2 seats per row. a) How many seats in Row 10? b) Write the rule for the number of seats in Row n. c) If there are 15 rows, how many total seats? (Hint: this is a growing pattern; find a way to sum without adding all 15 numbers one by one.)
- Create Your Own Pattern: Invent a visual pattern using shapes or colours that follows a clear rule (repeating, growing, or shrinking). Draw the first 5 steps. Write the rule. Exchange with a classmate (or family member) and have them write the next 2 steps and the rule they inferred. Attach their response.
Submission checklist
- Two real-world pattern sketches with rules identified
- Four number sequences extended with rules stated
- 10×10 grid with multiples of 4 shaded and written explanation
- Dot diagrams for first 5 triangular and 5 square numbers with labels and three written responses
- Skip-counting plot with three coloured lines and comparison sentence
- Assembly seating problem fully solved with work shown
Reflect on your learning
- How did using a grid help you see a pattern that was not obvious in a simple list of numbers? Give an example from your work.
- When you created your own pattern and someone else tried to extend it, did they find the same rule you intended? What does this tell you about how clearly a rule must be defined?
Completion requirements:
- Make a submission