Mathematical Thinking

48 Skills in Mathematics. 40 are ready to try — three verified questions each, no account needed.

Ready to try

Ages 5–6
Early Maths Vocabulary
Use mathematical words carefully when counting, comparing, and describing shapes and positions
9 verified questions on this shelf
Ages 5–6
Finding efficient methods
Notice when a calculation or pattern repeats and use this to count more efficiently or predict results
9 verified questions on this shelf
Ages 5–6
Hands-On Problem Solving
Select and use familiar tools (concrete objects, fingers, ten frames) to help solve a mathematical problem
6 verified questions on this shelf
Ages 5–6
Real-World to Maths Connections
Move between a real-world situation and a mathematical representation using concrete objects, drawings, diagrams, tables, number sentences, or bar models
9 verified questions on this shelf
Ages 5–6
Showing Your Working
Show and tell how a mathematical answer was found using objects, drawings, and spoken words
6 verified questions on this shelf
Ages 5–6
Using objects to model real problems
Use objects, drawings, or simple number sentences to represent a real-world situation (early mathematical modelling)
9 verified questions on this shelf
Ages 6–7
Connecting maths to real life
Represent real-world problems with number sentences, bar models, or diagrams, and interpret the mathematical result back in context
6 verified questions on this shelf
Ages 6–7
Connecting Representations
Move between real-world situations, drawings, and number sentences, explaining how each representation connects to the others (quantitative reasoning)
9 verified questions on this shelf
Ages 6–7
Explaining Mathematical Reasoning
With teacher prompting, explain and justify mathematical reasoning using drawings, number sentences, or words
9 verified questions on this shelf
Ages 6–7
Generalising Patterns
Recognise and use repeated reasoning to generalise: spot calculation patterns, describe rules for sequences, and predict results using known mathematical facts
13 verified questions on this shelf
Ages 6–7
Guided Multi-Step Problem Solving
With teacher guidance, make sense of multi-step and more complex problems by planning a pathway to the solution, identifying relevant information, and choosing appropriate operations
12 verified questions on this shelf
Ages 6–7
Shape patterns
Look for and use mathematical structure: apply properties of operations, place-value patterns, and relationships between shapes to solve problems efficiently
9 verified questions on this shelf
Ages 7–8
Choosing the right strategy
Select and use appropriate tools and representations strategically, including choosing between mental methods, jottings, formal algorithms, and calculators for arithmetic with multi-digit numbers, decimals, and fractions
8 verified questions on this shelf
Ages 7–8
Extending Table Patterns
Recognise and use repeated reasoning to generalise: extend multiplication table patterns, derive unknown facts from known ones, and describe rules for sequences
12 verified questions on this shelf
Ages 7–8
Justifying mathematical reasoning
Construct and follow multi-step mathematical arguments; identify errors in reasoning and explain why a method works or does not work
9 verified questions on this shelf
Ages 7–8
Multi-Step Problem Solving
With teacher support, make sense of multi-step problems involving larger numbers or mixed operations by breaking them into parts, choosing strategies, and checking answers for reasonableness — children at this stage are developing the habi…
9 verified questions on this shelf
Ages 7–8
Shape patterns (age 7+)
Look for and use mathematical structure: apply place-value patterns to three-digit operations, use multiplication/division relationships, and exploit shape properties to classify
9 verified questions on this shelf
Ages 7–8
Understanding fractions
Move fluently between real-world situations, diagrams, and symbolic equations involving three-digit numbers and fractions, explaining what each part represents
10 verified questions on this shelf
Ages 7–8
Understanding fractions (age 7+)
Communicate with mathematical precision: use correct place-value and fraction vocabulary, specify units in measurement answers, and use notation accurately
9 verified questions on this shelf
Ages 7–8
Working with money
Model real-world problems involving measurement, money, and time by choosing appropriate representations and interpreting results in context
9 verified questions on this shelf
Ages 8–9
Choosing mathematical tools
Select and use appropriate tools and representations strategically: choose between mental, written, and diagrammatic methods; use calculators for checking; select fraction models suited to the task
9 verified questions on this shelf
Ages 8–9
Fractions on a number line
Move fluently between real-world situations, diagrams, number lines, and symbolic equations involving multiplication, fractions, and decimals, explaining what each representation shows
21 verified questions on this shelf
Ages 8–9
Justifying mathematical reasoning (age 8+)
Construct and present multi-step mathematical arguments; critique the reasoning of others and explain clearly why a method works or fails
9 verified questions on this shelf
Ages 8–9
Mathematical Precision
Communicate with mathematical precision: use correct fraction/decimal vocabulary, name angle types accurately, specify units in measurement and money, and use notation (=, <, >, ÷, ×) correctly
9 verified questions on this shelf
Ages 8–9
Modelling with multiplication and fractions
Model real-world problems involving multiplication, area, fractions, and unit conversion by choosing appropriate representations and interpreting mathematical results in context
9 verified questions on this shelf
Ages 8–9
Times tables (age 8+)
Recognise and use repeated reasoning to generalise: extend patterns in times tables and equivalent fractions, derive unknown facts from known facts efficiently, describe general rules
9 verified questions on this shelf
Ages 8–9
Using Mathematical Structure
Look for and use mathematical structure: exploit place-value patterns for ×10/×100, use the distributive property to break apart multiplications, apply fraction equivalence to compare and compute, use shape properties to classify quadrilat…
9 verified questions on this shelf
Ages 9–10
Choosing representations strategically
Select and use tools and representations strategically: choose between mental methods, formal written methods, protractors, fraction strips, and diagrams based on the demands of the problem
9 verified questions on this shelf
Ages 9–10
Complex Multi-Step Problems
Make sense of complex multi-step problems involving large numbers, fractions, decimals, and percentages by analysing what is known and unknown, planning multi-step strategies, and evaluating reasonableness through estimation and inverse op…
10 verified questions on this shelf
Ages 9–10
Fractions on a number line (age 9+)
Move fluently between real-world situations, diagrams, number lines, bar models, and symbolic equations involving multi-digit multiplication, fractions, decimals, and percentages, explaining connections between representations
5 verified questions on this shelf
Ages 9–10
Fractions, Decimals & Percentages
Look for and use mathematical structure: exploit the relationship between fractions, decimals, and percentages; use factor pairs to simplify multiplication; apply angle facts to find unknowns; use properties of regular polygons systematica…
9 verified questions on this shelf
Ages 9–10
Real-World Maths Modelling
Model real-world problems involving scaling, unit conversion, area/perimeter, and percentage by selecting appropriate mathematical representations and interpreting results in context
9 verified questions on this shelf
Ages 9–10
Reasoning with Equivalences
Recognise and use repeated reasoning to generalise: extend patterns in equivalent fractions and percentage conversions, derive unknown facts from known facts, describe general rules for sequences and predict terms
9 verified questions on this shelf
Ages 9–10
Understanding fractions (age 9+)
Construct and present logical mathematical arguments involving multiple steps; critique others' reasoning about fractions, angles, or calculations and clearly explain errors or alternative methods
5 verified questions on this shelf
Ages 10–11
Advanced Maths Vocabulary
Communicate with mathematical precision: use correct vocabulary for ratio, proportion, algebra, volume, coordinate geometry, and circle parts; specify units including cm³, m³, and miles/km; use notation for algebraic expressions and order…
9 verified questions on this shelf
Ages 10–11
Advanced Multi-Step Problems
Make sense of complex multi-step problems involving ratio, proportion, algebra, negative numbers, and all four operations with fractions and decimals by analysing given and unknown quantities, planning solution strategies, and evaluating r…
9 verified questions on this shelf
Ages 10–11
Constructing mathematical arguments
Construct and present logical mathematical arguments involving multiple steps and formal reasoning; critique others' reasoning about fractions, algebra, ratio, or geometry and clearly explain errors or alternative approaches
5 verified questions on this shelf
Ages 10–11
Generalising with repeated reasoning
Recognise and use repeated reasoning to generalise: describe algebraic rules for nth terms, use properties of operations to simplify, and verify generalisations with specific cases
9 verified questions on this shelf
Ages 10–11
Order of operations (age 10+)
Look for and use mathematical structure: exploit the hierarchy of 2-D shapes to deduce properties; use order of operations and algebraic structure to simplify expressions; connect fraction–decimal–percentage equivalences; use ratio structu…
31 verified questions on this shelf
Ages 10–11
Understanding fractions (age 10+)
Move fluently between real-world situations, diagrams, coordinate grids, algebraic expressions, tables, and symbolic equations involving fractions, ratio, and algebra, explaining connections between representations
5 verified questions on this shelf

Being planted

These Skills are on the map, but their questions are still being written and checked.

Ages 5–6
Making Sense of Problems
Coming soon
Ages 5–6
Spotting mathematical patterns
Coming soon
Ages 6–7
Numbers on a number line
Coming soon
Ages 6–7
Precise Maths Communication
Coming soon
Ages 8–9
Multi-Step Problem Solving
Coming soon
Ages 9–10
Precise Maths Vocabulary
Coming soon
Ages 10–11
Choosing Maths Tools
Coming soon
Ages 10–11
Real-World Mathematical Modelling
Coming soon

Skill names and descriptions include the Marble Skill Taxonomy © Generative Spark, Inc. (withmarble.com), licensed under ODbL 1.0 (database) and CC BY-SA 4.0 (content). Practice questions are GlowGrades's own, each checked by independent verifiers that must agree before a child ever sees it.