NA3-8: Connect members of sequential patterns with their ordinal position and use tables, graphs, and diagrams to find relationships between successive elements of number and spatial patterns.
This means students will recognise that a sequential pattern can be either spatial, for example .., or numeric, for example 1, 3, 5, 7... A pattern has consistency so further terms of it can be anticipated from those already known. The focus in this thread is that students become increasingly sophisticated at describing the relationships between variables found in sequential patterns. With spatial patterns, students at Level Three should be able to identify the repeating element, for example , and use simple multiplicative thinking to predict the shape in a given ordinal position, for example Every third shape is so the thirtieth shape will be so the thirty-second shape will be With number patterns students should identify the consistent relationship between variables in simple multiple situations, for example 4, 8, 12, 16... are all multiples of four, or identify the additive “gap” between the terms, for example 4, 7, 10, 13... three is added each time. They should be able to describe these rules in their own words and use their rules to find further terms. Students also use tables, graphs, diagrams and word rules to find and describe relationships in patterns, for example
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“There is always one more peg than the number of towels. The first towel took two pegs.”
use a graph to look for a pattern
solve problems involving sequential patterns (Problems 1 and 4)
use simple multiplicative strategies to solve problems (Problem 2)
solve problems involving enlargements (Problem 3)
use addition to solve problem (Problem 3)
find the pattern for the number of diagonals in polygons (Problem 4)
- Predict the next term of a spatial pattern.
- Find a rule to give the number of matches in a given term of the pattern.
- Find the member of the pattern that has a given number of matches.
These Learning Outcomes are covered in every lesson of the unit.
make a three dimensional model with multilink cubes from a two dimensional drawing
describe and continue a sequential pattern
explore the Mayan number system
use tables to connect members of a sequential pattern
find outcomes using a tree diagram (Problem 1)
find rhombuses and trapezia in shapes (Problem 2)
continue a sequential pattern (Problem 3)
explore right angles on a clock face (Problem 4)
interpret three dimensional drawings
use a table to find a sequential pattern
continue a sequential pattern
continue a repeating pattern
find and apply rules for sequential patterns
describe a pattern using a rule or formula
use a rule to continue a pattern
find and apply rules for a sequential pattern
use a table to compete a pattern
find and generalise patterns in geometric patterns
use graphs to show relationships in sequential patterns
use rules to find unknowns in patterns
continue a sequential pattern (Problem 1)
share regions into fractions (Problem 2)
explore divisibility rules for 3 (Problem 3)
continue a sequential pattern
- Describe number patterns in words.
- Devise and use problem solving strategies to explore situations mathematically (guess and check, be systematic, make a drawing, use equipment).
- Describe number patterns.
- Solve problems involving patterns.
- Devise and use problem solving strategies (guess and check, make a table, look for patterns).
- Describe in words the rules for the pattern.
- Identify the pattern of triangular numbers.
- Devise and use problem solving strategies to explore situations mathematically (systematic list, draw a picture, use equipment).