| Math skill | Description | Manifestations of impaired skill | What to ask the school team |
| Number sense | - Ability to understand what is bigger or smaller, shorter or taller, etc
- Understanding that numbers are a precise way of knowing what is bigger, smaller, shorter, taller, etc
- Ability to visualize numbers in their correct order (ie, number line)
| - Does not understand differences in quantities
- Does not understand that numbers are a precise way of showing differences in quantities
- Inability to visualize numbers in their correct order (necessary for math operations)
| - Is this child developing number sense skills?
- Which number sense skills has this child developed?
- Which number sense skills is this child still mastering?
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| Math operations or math calculations | - Procedures for adding, subtracting, multiplying, dividing
| - Does not know how to perform all math operations or some math operations (eg, multiplication, division)
- Guesses at answers to math operations
- Makes errors in math operations
- May be able to perform math operations on single digits (eg, "3" or "7") but not on multiple digits (eg, "25" or "347")
| - Is this child able to perform addition and subtraction?
- How many digits can this child add and subtract?
- Is this child able to perform multiplication and division?
|
| Math fluency | - Ability to do math calculations smoothly and quickly
| - Takes a long time to perform math operations (math fluency is needed to perform multistep problems successfully)
| - Does this child have difficulty with math fluency?
|
| Math facts | - Automatically knowing the answer to common math calculations (crucial component of math fluency)
| - Cannot automatically remember the answers to common math calculations (eg, "25 + 5" or "7 × 7")
| - Does this child have difficulty with math facts?
|
| Complex math problems | - Multistep problems: Ability to perform calculations that have multiple steps
- Abstraction: Ability to use numbers to describe different types of quantities (eg, weight, volume, speed, money, time)
- Complex numbers: Ability to understand numbers such as fractions, decimals, and negative numbers
- Estimation: Ability to use knowledge of numbers to perform approximate calculations by making estimates
| - Difficulty with math problems that have multiple steps; steps may be carried out in the wrong order or performed incorrectly
- Inability to use numbers successfully when counting various quantities (eg, weight, volume, speed, money, time)
- Makes errors or guesses at the right answer without knowing how to solve the problem
| - Does this child have problems performing complex math problems?
- If so, is the problem due to:
- Problems in number sense?
- Problems in calculations?
- Problems with math fluency or math facts?
- Not doing all of the steps in the right order?
- Inability to abstract?
- Inability to use complex numbers?
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