Mathematics 7 linear patterns and relations
Specific Curriculum Outcomes
N01 Students will be expected to determine and explain why a number is divisible by 2, 3, 4, 5, 6, 8, 9, or 10, and why a number cannot be divided by 0.
PR01 Students will be expected to demonstrate an understanding of oral and written patterns and their equivalent linear relations.
PR02 Students will be expected to create a table of values from a linear relation, graph the table of values, and analyze the graph to draw conclusions and solve problems.
PR04 Students will be expected to explain the difference between an expression and an equation.
PR05 Students will be expected to evaluate an expression given the value of the variable(s).
N01 Students will be expected to determine and explain why a number is divisible by 2, 3, 4, 5, 6, 8, 9, or 10, and why a number cannot be divided by 0.
PR01 Students will be expected to demonstrate an understanding of oral and written patterns and their equivalent linear relations.
PR02 Students will be expected to create a table of values from a linear relation, graph the table of values, and analyze the graph to draw conclusions and solve problems.
PR04 Students will be expected to explain the difference between an expression and an equation.
PR05 Students will be expected to evaluate an expression given the value of the variable(s).
N01 Activities
 Divisibility Rock n' Rule  Divide the class into teams of three. Provide each team with four index cards and ask them to write a different digit between 0 and 9 on each card. Using the four different digits only once, each team will then make a list of all the possible fourdigit number combinations being sure to use each digit only once. There will be 24 possible number combinations. Using calculators if you wish, have the students divide each of their 24 numbers by 2, 3, 5, 6, 9 and 10 to decide if their numbers divide evenly without leaving remainders. If the number divides evenly, have the students record it in a chart. After this chart is complete, have each team record their check marked (yes) examples on chart paper hanging around the room, one piece for each of the numbers 2, 3, 5, 6, 9, and 10. Once this is done, have each team make a hypothesis about a “rule” for divisibility for each of the numbers 2, 3, 5, 6, 9, and 10. Have them record their hypotheses and then discuss as a class. Compare the class rules to the common divisibility rules.
 Divisibility Laws and Raffle Tickets from Jason Steele  Students are given a handful of tickets and work in pairs to place the them in the correct area in Venn diagrams (e.g. divisible by 2 and divisible by 3). Groups of students can explain what they see from looking at the numbers in the intersections of the Venn diagrams. (If we knew a number was divisible by 2, and divisible by 3, then it would be divisible by 6). Nice use of Venn diagrams to get students to notice some of the divisibility rules on their own.
 Sierpinski Triangle Patterns  Colour all the numbers in a Sierpinski triangle that are divisible by two... what do you notice. What if instead you coloured all the numbers that are divisible by three? An interesting pattern emerges.
 Dozens from NRICH  An online activity in which the computer generates two random digits. Your task is to find the largest possible threedigit number which uses the computer's digits, and one of your own, to make a multiple of 2, 3, 4 or 6. For example, what is the largest three digit number divisible by six that includes the digits 7 and 2?
 Divisibility  Take 10 cards numbered 0 to 9. Each time use all ten cards. Arrange the cards to make (a) five numbers that are divisible by 3, (b) four numbers that are divisible by 4, (c) five prime numbers. Make up your own additional divisibility challenges that use all ten cards to make special numbers.


 The Factor Game or The Taxman Game  Two different versions of the same game that will let students practice their divisibility/factoring skills. Two players or teams take turns selecting a number from 1 to 30 (or some other number). The first player/team chooses a number. This is their score for that round. The second player/team determines all the proper factors of the first player/teams's number. The sum of those factors is the second player/team's score for that round. Keep alternating until all possible numbers have been used.
 Is it Prime? Game  Use your new skills with divisibility to see how many prime numbers you can identify in this simple online game.
 Digits and Primes from Henry Dudeney  Using the nine digits once, and once only, can you find prime numbers (numbers that cannot be divided, without remainder, by any number except 1 and itself) that will add up to the smallest total possible? Here is an example.61+283+47+59=450. The four prime numbers contain all the nine digits once, and once only, and add up to 450, but this total can be considerably reduced.
 Why Can't You Divide by 0 from Math With Bad Drawings  A nice explanation of why you can't divide by 0. I especially like the link to the Billy Preston explanation left in the comments.
 American Billions from Nrich  Two students play a divisibility game with a set of 0  9 digit cards. They take it in turns to choose and place a card to the right of the cards that are already there. After two cards have been placed, the twodigit number must be divisible by 2. After three cards have been placed, the threedigit number must be divisible by 3. After four cards have been placed, the fourdigit number must be divisible by 4. And so on! They keep taking it in turns until one of them gets stuck. A poster is here.
PR01 Activities
 Visual Patterns from Fawn Nguyen  There are loads of visual patterns for students here. Each image shows the first three steps of a pattern and how many elements there are in the 43rd step. Students can describe the patterns with both words and an equation and then test their equation for the answer for the 43rd step. Caution... not all of these patterns are linear.
PR02, PR04 and PR05 Activities


 Knot Again from Jon Orr and Knots of Different Thickness and Equal Length from Alex Overwijk  Take a rope. Tie some knots in it. How much shorter is the rope each time you tie a knot? Predict how short the rope will be after you tie 10 knots. Tie the knots and see how close you are. Can you come up with an equation for the length of the rope given n knots?
 Central Park by Desmos  Central Park asks students to design parking lots. At first, students place the dividers by hand, then they calculate the distance from given measurements, then they create a formula using variables.