As caregivers, it can be very challenging to ascertain exactly what goals your child needs to meet at any given age or grade. To help, we’ve compiled a list of the most common math developmental milestones for elementary, middle, and high school learners to serve as a reference as you work your way through each phase of your learner’s academic journey. It is important to note that everyone progresses at their own pace, so please keep this in mind as you review the grade and age-specific markers below.
The Mathematical Ladder
Learnfully utilizes the math ladder as a tool to guide our Educational Specialists and community as a whole towards foundational and application of math skills.
Math Resources
- General Information
- Early Education
- Math Milestones
- Manipulatives for Teachers
- Piaget’s Stages of Cognitive Development
- Math Developmental Milestones
General Information
Early Education
- Mrs Meyers Math Milestones For Kids By Age
- Sesame Street: Children’s Math Development
- Nurtured Neurons: 7 Simple Ways To Develop Preschool Math Skills
Math Milestones
- Math Milestones Grade-Level Grids
- Math Concepts and Skills by Age
- Understood.org: Math skills at different ages
- Mathematics milestones
Manipulatives for teachers
Piaget’s Stages of Cognitive Development
|
|
|
|||
|---|---|---|---|---|---|
| Sensorimotor | 0-2 years old | Coordination of senses with motor responses, sensory curiosity about the world. Language used for demands and catalouging. Object permanence is developed | |||
| Preoperational | 2-7 years old | Symbolic thinking, use of proper syntax and grammar to express concepts. Imagination and intuition are strong, but complex abstract thoughts are still difficult. Conversation is developed. | |||
| Concrete Operational | 7-11 years old | Concepts attached to concrete situations. Time, space, and quantity are understood and can be applied, but not as independent concepts. | |||
| Formal Operational | 11 years and older | Theoretical, hypothetical, and counterfactual thinking. Abstract logic and reasoning. Strategy and planning become possible. Concepts learned in one context can be applied to another. |
Math Developmental Milestones
|
|
|
|||
|---|---|---|---|---|---|
| 5-6 | Kinder | Add by counting the fingers on one or both hands. | |||
| Follow multi-step directions. | |||||
| Begin to understand basic time concepts. | |||||
| Copy or draw symmetrical shapes. | |||||
| Identify the larger of two numbers. | |||||
| Understand the meaning of words like unlikely or possible. | |||||
| 6-8 | 1st-2nd | Count to 100 by ones, twos, fives, tens. | |||
| Write and recognize the numerals 0 to 100, and the words for numbers from one to twenty. | |||||
| Know the difference between two and three dimensional shapes and name the basic ones. | |||||
| Recognize and know the value of coins. | |||||
| Predict what comes next in a pattern and create own patterns. | |||||
| Compute basic addition and subtraction up to 20. | |||||
| Read and create a simple bar chart. | |||||
| 8-9 | 3rd | Move from using hands-on methods to using paper and pencil to work out math problems. | |||
| Do addition and subtraction with regrouping. | |||||
| Understand place values well enough to solve problems with decimal points. | |||||
| Know how to multiply and divide using fact families. | |||||
| Create a number sentence or equation from a word problem. | |||||
| Work with money. | |||||
| 9-11 | 4th-5th | Understand that numbers can be represented in many ways like fractions, decimals, bases and variables | |||
| Use numbers in real-life situations like calculating a sale price or comparing student loans. | |||||
| Use mathematical language to convey thoughts and solutions. | |||||
| Use graphs, maps, or other representations to learn and convey information. | |||||
| Begin to understand that some math problems do not have real-world solutions. | |||||
| Begin to see how math ideas built on one another. | |||||
| 11-18 | 6th-12th | Basic and complex algebra with unknown numbers. | |||
| Work with lines, angles, types of triangles and other basic geometric shapes. | |||||
| Work with fractions, percentages, and proportions. | |||||
| Use formulas to solve complicated problems and find the area, permitter, and volume of shapes. |
