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
“There is always one more peg than the number of towels. The first towel took two pegs.”
explore patterns (Problem 1)
solve problems involving transformations (Problem 2)
use addition skills to solve problems relating to distances (Problem 3)
solve problems using addition (Problem 4)
use a graph to show relationships in sequential patterns
use a table to find and predict patterns
- Continue a linear growth pattern from a few examples.
- Find the recursive rule of a linear growth pattern from table of values.
- Explain why the graph of relationships in the pattern is linear.
- Use the table and recursive rule, and/or the graph to make predictions about other terms of the300
find volume of a cuboid (Problem 1)
continue a sequential pattern (Problem 2)
solve division problems (Problem 3)
use algebraic thinking to solve problems (Problem 4)
interpret and draw representations of cube patterns
identify the pattern in a series of cube buildings
use a table to find a rule for a geometric pattern
write rule to describe a relationship
- Use a ‘cups and cubes’ model to describe relationships.
find a relationship in a number pattern
Explaining the pattern in a set of numbers in words.
continue a sequential pattern
solve multiplication problems using palce value knowledge and basic facts
apply a rule
interpret timezones information
find and use rules in number patterns
find a number rule
use a symbols to express the rule
find a rule to describe a relationship
complete a sequential pattern
show data on a line graph
use a table to find a rule
use mental strategies to add numbers
use addition and multiplication to solve problems (Problem 1)
continue a sequential patterns (Problem 2)
interpret relationships from a graph
continue a sequential pattern
- identify the relationship between the relative positions of weights, the centre of gravity of the system, and stability.
Students should discover that:
- the turning force (moment around the fulcrum) produced by gravity is a function of weight x horizontal distance from the fulcrum.
- as the300
use addition strategies to solve problems (Problems 1 and 4)
find outcomes using a table or diagram (Problem 2)
continue a pattern (Problem 3)
use a graph to look for a pattern