The Year 5 Multi-Step Addition and Subtraction Problems PowerPoint guides both teachers and children through the lesson, including use of the varied fluency, reasoning and problem solving, deeper reasoning and scaffolded resources. Key learning information about this step:
Key Vocabulary
multi-step problems: Maths problems that have more than one operation. An example may include both an addition and a subtraction.
bar models: Show how numbers can be split into different parts, by splitting them into bars or boxes. Bar models can be used to solve a wide variety of calculations, showing the relationship between the whole model and the parts.
inverse operations: Used to check working out or to find a starting number by using the opposite operation. Addition is the inverse of subtraction and vice versa. Multiplication is the inverse of division and vice versa.
Varied Fluency
Knowledge Organiser
• Designed to support all children via key information and examples.
For the purple sections of the four levels, copy and paste these from the first sheet of the varied fluency resource.
Scaffolded Examples
• Reading a problem, then adding each amount in turn to find the total.
Support
• Q1: Add three 5-digit numbers to find a total; no exchanges; parts completed in bar model, work out whole.
• Q2: Use a bar model to find the missing part; two parts given; 5-digit numbers; no exchanges in addition, one exchange for subtraction; steps given to support.
• Q3: Three-step problem; 5-digit numbers; one exchange in addition and subtraction; three steps given.
Core
• Q1: Add three 5-digit amounts to find a total; one exchange; empty bar model.
• Q2: Use a bar model to find the missing part; 5-digit numbers with up to 3 exchanges; empty bar model given.
• Q3: Three-step problem; 5-digit numbers with exchanges.
Stretch
• Q1: Add three 5-digit amounts to find a total; with up to 3 exchanges.
• Q2: Find the missing part; 5-digit numbers, up to 4 exchanges inc. through 0.
• Q3: Three-step problem; multiple exchanges including through 0.
Reasoning and Problem Solving
Support
• Q1: Reasoning – deciding whether a character’s plan for a three-step problem is correct; 5-digit starting amounts; accessible calculations
• Q2: Reasoning – matching a problem to a bar model; 5-digit whole and two known parts given; one missing part; accessible place-value structure.
• Q3: Problem Solving – finding three possible pairs of amounts sent; accessible number structure supports children to identify the total sent before finding different pairs.
Core
• Q1: Reasoning – deciding whether a character’s plan for a three-step problem is correct; 5-digit numbers with exchanges.
• Q2: Reasoning – matching a problem to a bar model; 5-digit whole and parts; exchanges in both steps.
• Q3: Problem Solving – finding three possible pairs of amounts sent; less accessible number structure, need to independently calculate the total sent before finding different pairs.
Stretch
• Q1: Reasoning – deciding whether a character’s plan for a three-step problem is correct; one amount must first be found by halving; 5-digit numbers.
• Q2: Reasoning – matching a problem to a bar model with an unknown whole; three parts represented; one part may need to be found by halving.
• Q3: Problem Solving – finding three possible sets of values; two amounts sent and the delivery are unknown; relationship between three variables.
Deeper Reasoning
The questions in this set focus on problem solving with multi step problems to identify totals and find remaining amounts to deepen understanding in solving addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why.
