These exercises, activities and games are designed for students to use independently or in small groups to practise number properties. Some involve investigation (Mikes Investigation Sheet link) and may become longer and more involved tasks with subsequent recording/reporting.
generalise a number pattern
Multiplication and Division, AM (Stage 7)
calculator
Prior Knowledge:
- complete an easy Sudoku puzzle
Background:
These exercises use the structure of the common Sudoku puzzle to explore the sums of patterns of numbers. It is important that students know that each row, each coloumn and each 3x3 block of 9 in the puzzle all have the same sum. The puzzles drawn may be completed by students although it is the same one altered for each different set of numbers. Exercise 8 is a summary sheet which serves as a self check. The final code is 02 453 472.
Note a sequence is an infinite list of numbers such as 1,2,3,4,5… such that the pattern is obvious. A series is the sum of a finite sequence for example 1 + 2 + 3 + 4 + 5… n.
Further information to back up what they will meet:
- FIO Books – eg Basic facts level 3, p13
- National Archive of Virtual Manipulatives (via Google “nlvm”) Grade 6-8 Number, Fibonacci Sequence, and Golden Ratio.
Comments on these exercises
Exercise 1
Asks students to solve the Sudoku puzzle using numbers 1-9, and to generalise the number patterns.
Exercise 2
Asks students to solve the Sudoku puzzle using the first 9 odd numbers and to generalise the number patterns.
Exercise 3
Asks students to solve the Sudoku puzzle using the first 9 even numbers and to generalise the number patterns.
Exercise 4
Asks students to solve the Sudoku puzzle using the first 9 multiples of 3 and to generalise the number patterns.
Exercise 5
Asks students to solve the Sudoku puzzle using the first 9 powers of 2 and to generalise the number patterns.
Exercise 6
Asks students to solve the Sudoku puzzle using the first 9 multiples of 9 and to generalise the number patterns.
Exercise 7
Asks students to solve the Sudoku puzzle using the first 9 multiples of 9 and to generalise the number patterns.
Asks students to solve the Sudoku puzzle using the first 9 square numbers and to generalise the number patterns.
Exercise 8
Asks students to complete the puzzle using answers from previous Sudoku puzzles answers.