Short Blocks

Maths Year 5/6 Spring Algebra and Ratio

Each unit has everything you need to teach a set of related skills and concepts.

Algebra (suggested as 4 days)

Planning and Activities

Day 1
Show how n can be used to stand for the width of a garden in order to calculate different areas of turf.
Group Activities: T with Y6
Y5 -- Begin to identify rules for function machines. Or, write and use formulae to calculate ages.
Y6 -- Write formulae for questions. Or, play ‘Guardians of the rule’ as a group (a game to deduce 2-step rules).

Day 2
Write 25 + a = 30 and sketch a bar model to show this. Calculate what a represents. Repeat with similar equations.
Further Teaching with Y6
Write a + b = 10, explaining that a and b are two new mystery numbers. List possible whole answers. Repeat with similar equations.
Group Activities: T with Y6
Y5 -- Deduce the numbers represented by letters in a multiplication grid. Or, solve equations with missing numbers, and write similar equations.
Y6 -- Solve a series of equations by finding successive unknowns. Or, find pairs of numbers which satisfy two equations with two unknowns.

Day 3
Display 2, 4, 6, 8 .... Show how we can use the relationship between the number of the term and its value in the sequence, i.e. each value is 2 times the term number. Calculate the 10th term and the 100th term. Repeat with other linear sequences, recognising the times table they are based on. Describe an nth term for each sequence algebraically.
Group Activities: T with Y6
Y5 -- Identify steps and missing numbers in sequences.
Identify step increase or decrease, including sequences which pass through zero, or with decimal steps.
Y6 -- Find the 10th term, 100th term, then nth term in linear sequences. Or, create linear sequences based on 10n, writing an expression for the nth term.

Day 4
Make a sequence of shapes from multilink (see download); use these to generate a linear numerical sequence. Find the value of the 10th term; describe what is happening in words, then write an algebraic expression or general rule for the nth term.
Group Activities: T with Y5
Use the in-depth problem-solving investigation ‘Stars and Crosses’ as today’s group activity.
Or, use these activities:
Y5 -- Investigation of a pattern of shapes: identifying/describing shapes further in the sequence without making all the shapes up to that point.
Y6 -- Investigation of a pattern of shapes: identifying/describing the 10th and nth terms.

You Will Need

  • ‘Garden sketch’ (see resources)
  • ‘Function machines 1’ (see resources)
  • ‘Write a formula’ (see resources)
  • ‘Function machines 2’ (see resources)
  • ‘Sequences’ (see resources)
  • Flipchart and pens
  • Sticky notes
  • Multilink cubes
  • SATs-style questions (see download)

Short Mental Workouts

Day 1
Equivalence

Day 2
Function machines

Day 3
Counting back

Day 4
Sequences

Worksheets

Day 1
Y5: Identify functions and write outputs in terms of n.
Y6: Write and use simple formulae.

Day 2
Y5: Solve equations, including bar model and geometry examples.
Y6: Solve equations, including bar model and geometry examples; list solutions for equations with two unknowns.

Day 3
Y5: Complete sequences by deducing their step increase/ decrease.
Y6: Find the 10th, 100th then nth term for sequences.

Day 4
Y5: Draw the next ‘Y’ or ‘V’ shape in a sequence. Find a relationship between the number of shapes in the pattern and its position in the sequence.
Y6: Draw the next ‘spinner’/ ‘staircase’ in a sequence. Find a relationship between the number of shapes in the pattern and its position in the sequence.

Mastery: Reasoning and Problem-Solving

Y5/Y6

  • If the perimeter of a regular shape is 5 × n, where n is the length of a side, what is the shape? Find the perimeter when n = 6.5cm.
  • Darren draws a function machine. It trebles a number and then subtracts 6. Sophie sees that one of the outputs is 15. What was the input? Then Darren inputs 11. What output will Sophie see? Write the formula for Darren’s machine.
  • Formula A is 3n.
    Formula B is n + 6.
    What number can n represent which will make these two formulae equal the same amount?
  • 2a is 5 more than 3b. If a and b are both whole numbers and a < 10, what are the possible values for a and b?
  • The 4th term of a sequence is 17, the 5th is 21 and the 6th is 25. Write the next four terms. Then write the first three terms. What is the nth term in this sequence?

In-depth investigation: Stars and Crosses
Children find totals of the numbers in shapes on a 1–1 00 grid, make generalisations and then write a formula to find the total of any similar shape on the grid.
A presentation is available to guide children through the investigation.

Extra Support

Y5/Y6
Mathematical Mysteries
Solving equations using the bar model.

Spot the rule
Counting sequences