Connected foundations
Topics progress from matching and counting to arithmetic, fractions, algebra and calculus, connecting new ideas with previous learning.
THE BACKBONE OF MATHEMATICAL THINKING
Understand maths.
Think clearly.
Go further.
Mathematics programs for ages 4 to 18 years
Build a strong foundation from Pre Level to Level 14
Let’s explore with Robo ↗ Try a learning experience ↗ 15 levels · Starting at age 4 · Built on understanding
Small discoveries. Deeper understanding. THE MATHBONE MOMENT
A STRONG FOUNDATION. A CURIOUS MIND.
A strong foundation starts with understanding
From numbers and shapes to more complex problems, explore the curriculum, learning approach and examples that suit the learner.
WHY MATHBONE
Understand mathematics and build skills for the next step
From early activities to more complex problems, MathBone focuses on understanding, reasoning and application.
Objects and pictures that explain
Counters, ten frames, fraction strips and models reveal relationships before connecting them to numbers and equations through CPA.
Room to explore
Missions invite learners to arrange, rotate, observe and plan, trying their own strategies and using hints when needed.
Reasoning that can be explained
Learners explain their thinking, compare strategies and check whether an answer makes sense in context.
Notice what learners understand
Practice, activities and checkpoints help identify independent understanding and skills that need further practice.
ROBO · MATHBONE Your curious companion
Explore with Robo
ideas that grow
A little companion who invites you to try, observe and explain. Explore numbers and shapes, and discover your own way of thinking.
There’s no need to rush
Try a different angle first
Start a mission with Robo ↗ Try a different angle first
The MathBone way · CPA
Explore with real objects.
Think with pictures.
Connect with equations.
CPA means Concrete, Pictorial and Abstract: connecting the same idea through objects, pictures and symbols. Learners can return to pictures or objects whenever they need support.
A learning example How can we think about 8 + 5?
Split 5 into 2 and 3, complete a group of ten, then add what remains.
C CONCRETE
Handle objects and explore
Arrange 8 counters and 5 more. Move 2 to complete the first group of ten.
The learner arranges, splits and combines the objects. P PICTORIAL
See relationships in pictures
Use a ten frame or number bond to show that 5 splits into 2 and 3 while the total stays the same.
The picture shows the part making ten and the part remaining. A ABSTRACT
Explain with symbols
Write an equation from the experience and explain what each number represents.
8 + 5 = 8 + 2 + 3 = 10 + 3 = 13
Robo invites you to connect what you see
Explain how the counters, pictures and numbers in the same problem are connected.
Apply the idea to a new problem How could the same strategy help with 28 + 5?
Discover · Play · Understand
Explore and discover
MathBone thinking
Begin with what you can see, connect it to an idea and apply it to a new problem. Explore at your own pace.
All 5 missions explored! Explain the ideas in your own words, then discover what you could explore next at MathBone.
Explore the curriculumSample website activities. No account needed. Progress lasts only while this page stays open.
Little discoveries. Lasting foundations.
Learn by doing
opens up new understanding
Explore numbers, investigate shapes and explain your reasoning. Small questions lead to ideas that grow.
Explore by doing
See what numbers mean
Arrange, split and combine. Connect the models you see with equations you understand.
Explore numbers ↗ Explore by seeing
A new angle, a new way to think
Rotate, reflect and compare. Explore relationships between positions and shapes.
Explore shapes ↗ Explore by reasoning
Give reasons for your choices
Plan a path, test the conditions and explain why you chose that approach.
Explore reasoning ↗Every age. A new possibility.
Every age has
A starting point for your child.
For learners aged 4 to 18, with 15 progressive levels. Choose a starting point based on understanding and readiness.
FOUNDATION /01
4 to 6 years
Start with curiosity
Matching, counting, shapes and patterns through hands-on exploration and meaningful pictures.
Pre Level to Level 2
DISCOVERY /02
7 to 12 years
Discover their own way of thinking
Connect numbers with calculation, use models to solve problems, and explore fractions, decimals and ratios.
Level 3 to Level 8
ADVANCED /03
13 to 18 years
Progress to advanced mathematics
Algebra, graphs, functions and advanced mathematics leading to calculus and data analysis.
Level 9 to Level 14
Ages are a guide. Learners with an existing foundation can start at a level suited to their readiness.
For growing minds
Mathematics for older learners
Develop think deeper.
For ages 13 to 18, Levels 9 to 14 connect algebra, geometry, functions and advanced mathematics, helping learners choose strategies and explain reasoning.
- Represent real situations with equations and graphs.
- Use geometric properties and evidence to explain.
- Progress to differentiation, integration, probability and statistics.
FROM IDEAS TO REASONING A glimpse of the mathematics
Sample problems
that invite you to think further.
Examples of topics for older learners. Explore the diagrams, ask questions and reveal each explanation.
Level 10 Explore curriculum topics ↗
See equations through graphs
Where does y = x² − 4 cross the x-axis?
Reveal the reasoning and answer
Set y = 0 to get x² = 4. Then x = −2 or 2, so the intercepts are (−2, 0) and (2, 0).
Level 10 Explore curriculum topics ↗
Geometry explained with reasoning
A right triangle has legs of 3 cm and 4 cm. How long is the hypotenuse?
Reveal the reasoning and answer
By Pythagoras, c² = 3² + 4² = 25. Length is positive, so c = 5 cm.
Level 13 Explore curriculum topics ↗
Calculus and change
If f(x) = x², what is the tangent slope at x = 2?
Reveal the reasoning and answer
The derivative is f′(x) = 2x. At x = 2, f′(2) = 4, so the slope is 4.
YOUR FIRST STEPS
Getting ready to begin
Choose a starting point based on readiness and discuss learning goals and practical details with the team.
Share background and interests
Share age, school year, current topics and areas where support is needed, such as number understanding, word problems or explaining reasoning.
Explore the level descriptions
Read the Pre Level to Level 14 topics and note familiar areas and practice needs. Ages are guidance, not placement rules.
Confirm details before enrolling
Ask the team about centres, schedules, fees, session counts and course terms to find a suitable arrangement.
Curiosity, on paper
Great ideas
can start with one sheet of paper.
MATHBONE JOURNAL
From primary to secondary: understand the reasoning
Explore primary fractions and ratios, then secondary equations, graphs, geometry and probability, with worked steps and explanations.
Articles 1 to 3 of 26
View all articles ↗ Primary
Upper primary · Fractions
Fractions of fractions: how much of a 3/4 m ribbon remains?
Start with equal parts, then solve a multi-step problem and identify the whole at each step.
Read article ↗ Secondary
Lower secondary · Simultaneous equations
Two conditions, one solution: simultaneous equations
Understand the intersection before eliminating a variable.
Read article ↗
Secondary
Lower secondary · Quadratics
Factoring and graphs: why are there two solutions?
Connect x² − 4x + 3 with its factors, intercepts and minimum.
Read article ↗ Foundations and learning approach
Singapore Math · CPA
CPA in Singapore Math: from objects to pictures and equations
Connect three representations of one idea with a practical 8 + 5 example.
Read article ↗
Foundations and learning approach
The CPA approach
From objects to equations: CPA at home
Connect everyday objects, drawings and a short equation to the same idea.
Read article ↗
Foundations and learning approach
Numbers and addition
Why does making ten help with addition?
Use a ten frame to see a missing part before connecting it to addition.
Read article ↗
Foundations and learning approach
Thinking with models
One number, many number bonds
Connect parts with the whole through objects and a simple diagram.
Read article ↗
Primary
Upper primary · Multi-step problems
Equal after a transfer: use a bar model to find the original amounts
When one amount falls and the other rises, how does the gap change? Model it before calculating.
Read article ↗
Primary
Multiplication
See multiplication through rows and columns
Arrange equal groups and connect them with multiplication.
Read article ↗
Primary
Upper primary · Ratios and units
A 2 : 5 ratio and a 1.4 L mixture: find each amount
Connect a ratio, fractions of a total and litre-to-millilitre conversion in one problem.
Read article ↗
Foundations and learning approach
Curriculum
How do you choose a starting level?
Age offers a guide; prior knowledge and readiness make the conversation more useful.
Read article ↗
Primary
Shapes and reasoning
What can rotation and reflection help us explore?
Explore position, comparison and change through a short visual game.
Read article ↗
Secondary
Mathematics for older learners
Making sense of algebra through models
Connect a simple situation with words, variables and a graph before increasing complexity.
Read article ↗
Foundations and learning approach
For parents
Three questions to ask after a mistake
Use a difficult moment for reflection while keeping the thinking with your child.
Read article ↗ Foundations and learning approach
Early learning
Everyday objects make counting meaningful
Match objects one by one and explore what the final count means.
Read article ↗
Foundations and learning approach
Patterns
Find the rule before guessing what comes next
Explore colours and shapes before connecting to number patterns.
Read article ↗
Primary
Measurement
Where should a ruler measurement begin?
Length is a distance, not just the number beside an object’s end.
Read article ↗
Primary
Time
Connect telling time with everyday routines
Use a clock and timeline to explore starting times and elapsed time.
Read article ↗
Primary
Everyday mathematics
A pretend shop for money and change
Connect prices, payment and differences through pretend play.
Read article ↗
Primary
Upper primary · Decimals
Why does 7.5 bottles mean you need 8?
Calculate capacity with decimals, then interpret the result as a whole number of bottles.
Read article ↗
Secondary
Graphs and data
Before interpreting a graph, read the axes
Check units, range and scale before drawing a conclusion.
Read article ↗
Secondary
Advanced mathematics
Derivatives begin with “How fast is it changing?”
Connect a graph, its slope and a rate of change.
Read article ↗
Secondary
Lower secondary · Equations
Solve 3(2x − 1) = 4x + 9 and justify each step
Connect a balance model with expanding brackets and checking by substitution.
Read article ↗
Secondary
Lower secondary · Geometry
Find a missing side and connect it to area
Identify the hypotenuse before applying a² + b² = c².
Read article ↗
Secondary
Lower secondary · Probability
Drawing without replacement: why does the second chance change?
Use a tree diagram to follow outcomes and multiply along a path.
Read article ↗
Secondary
Lower secondary · Statistics
Mean or median: which better describes the data?
Use one data set to see how an unusually large value affects summaries.
Read article ↗Scroll right for more articles, or use the arrow buttons
Questions parents may have
Does everyone start at Pre Level?
No. The curriculum begins at Pre Level, but the starting point should reflect prior knowledge and readiness. Discuss level selection with the team.
What can a fluent calculator practise?
Alongside answers, learners can practise reasoning, modelling, comparing methods and solving problems with new conditions at their level.
How can a less confident learner begin?
Start with familiar ideas, use pictures or objects and gradually add complexity. Tell the team which areas are independent and which need support.
Do 48 booklets mean 48 lessons?
No. The 48 core booklets describe curriculum materials per level. Session counts and teaching hours depend on the offered course.
Can Math Lab determine placement?
Math Lab offers sample activities for exploring ideas. It is not a placement test or a formal learning assessment.
Where can I ask about fees and schedules?
Use the MathBone contact form with the learner’s age and preferred area. The team can respond with relevant course details.
YOUR CHILD’S NEXT CHAPTER Your child’s next chapter
Your child’s next chapter
starts with understanding today.
Programs for ages 4 to 18, from Pre Level to Level 14. Find a path suited to understanding and readiness.