Essential Math Terms, Concepts + Tools for Your Child

Understand how to help your child with math skill development and learn common math terms and strategies that teachers use. Foundational early math concepts in one simple tip sheet.

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Basic Concepts

Understanding primary concepts used by teachers helps parents understand the development of math skills and provides insight into how children build their own conceptual understanding about math. Gone are the days of rote memorization and vertically adding and subtracting numbers.

There are some key things to remember when teaching your child math, including common math terms that are core and foundational to math learning. Although the modern math ‘Landscape of Learning’ for children is complex and nonlinear, learning these terms, ones you may hear your child’s teacher reference and that showcase just how non-sequential math learning can be, can aid in identifying where to specifically support your child.

Key Math Terms and Strategies

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Terms and Strategies	Concept Definition	Why it’s Mathematically Important to Know this Term	Learning Tools
Automaticity / Fluency	Quick recognition of basic facts which quickly become Helper Facts when problem solving. Being efficient, accurate and flexible are equally important.	For example: 3+7 helps a child solve, 4+7, 13+7, 23+17 and so on. If a child knows 3×3, they can use it to solve 3×4. 4×4 can be doubled and halved to find 2×8.	10-frame Tally marks – 5, 10 structure Number line Rekenrek
Base 10	The underpinning of our number system (with the exception of the American measurement system). The idea that ten ones make 10, 10 tens make 100, 10 hundreds make a thousand, and so on.	The use of base 10 models allows a child to manipulate the number system in a hands-on way.	Base 10 model Tally marks – 5, 10 structure Hundreds board
Cardinality	A counting and quantity principle that refers to the understanding that the last number name counted represents the number of objects counted in a set of objects. For example, the set P = {2, 4, 6} has 3 objects so P has a cardinality of 3.	If a child is asked, “How many marbles are in this jar?” they are linking counting to cardinality. The number of marbles in the jar is the same regardless of the arrangement or order in which the marbles are counted.	Manipulatives
Compensation (or Giving Strategy)	Changing a number (finding equivalences) to make it easier to work with mentally.	For example, when adding 39+22, compensation would be: adding 40+22 and then subtracting 1, or taking one from 22 so the new problem would be 40+21. Alternatively, 8+6 can become 7+7 by giving one from the 8 to the 6.	Manipulatives Rekenrek
Conservation	The number of objects is the same even when objects are rearranged.	The number name means an amount, and that amount stays the same.	Manipulatives Rekenrek
Count Efficiently	Count in groups of 10.	Build a knowledge base in the Base 10 system. When counting, first consider how many groups of ten, then how many loose units/ones. Next, consider how many more loose units/ones are needed to make another group of ten.	Base 10 model Tally marks – 5, 10 structure
Decomposition	Taking a number apart in a way that emphasizes the different values of each digit. For example, decomposition of 163 is 100+60+3.	Decomposing numbers is useful when using a strategy called partial sum addition – when a child adds larger numbers together by breaking them down. 245 + 122 would be solved by adding (200+100) + (40+20) + (5+2).	Number line Base 10 model Rekenrek
Doubles Facts	When a number is added to itself. For example, 2+2, 5+5, 8+8, 10+10 are all Doubles Facts. Doubles Facts allow a child to be a flexible problem solver because Double Facts become Helper Facts.	Once a child knows their Doubles Facts, they can quickly learn other facts and automaticity is increased. For example, 6+6 helps you solve 6+7 (doubles +1), 5+6 is doubles -1, 16+6 is doubles +10, etc. Early learners should learn Doubles Facts up to 20.	Rekenrek
Estimation	A ‘best guess’ calculation that does not involve counting; requires a child to use what they know to roughly judge a value or amount.	After calculation, estimation is one of the most used math skills. Helps build number sense, and requires problem solving and critical thinking.	Manipulatives
Friendly Numbers (or Landmark or Benchmark Numbers)	Typically consists of 10 and multiples of 10; makes working with larger numbers in equations easier.	This strategy allows a child to see the tens inside of numbers when they decompose, and then mentally add and subtract. For example, in solving 28+14, a child could add two to 28 as it is easier to add 30+14, and then subtract the two at the end.	10-frame Number line Base 10 model
Helper Facts	The baseline facts a child should know quickly that can be used to solve unknown facts.	If a child knows 6+6, they can apply that to 6+7. If a child knows 10+8, they can solve 9+8. Examples of Helper Facts: Doubles Facts and Ten Facts.	10-frame Tally marks – 5, 10 structure Number line Rekenrek
Magnitude	Ordering numbers with a true understanding for the quantity in a number name and the relationship between numbers and quantities.	For example, 15 is 5 more than 10.	Manipulatives Rekenrek Base 10 model
Mental Math	A set of skills that allows a child to do math ‘in their head’ without using pencil and paper or a calculator. Being efficient, accurate and flexible are equally important.	A child’s ability to do mental math ranges and for some children, increases with repeated exposure to concepts.	10-frame Tally marks – 5, 10 structure Number line Rekenrek
Number Sense	A set of skills that enable a child to work with numbers. Allows a child to use what they know to solve what they do not know. It is a sense of what numbers mean.	Understanding quantities – grasping concepts like more and less, and larger and smaller. Recognizing relationships between single items and groups of items – decomposing numbers, using helper facts to flexibly solve problems.	Manipulatives Rekenrek Base 10 model
1:1 Correspondence	The understanding that every object in a set can only be counted once; the ability to match one object to one (corresponding) number.	For example, when a child counts objects, they pair each object with one and only one number name and each number name with one and only one object. Avoids double counting (the pairing of more than one number name to an object).	Manipulatives Hundreds board
Place Value	The value of each digit in a number: thousands, hundreds, tens, units/ones. For example, in ‘4,272’, the place value of the ‘7’ is tens.	Teaching what we call the standard algorithm and not the concept can confuse a child who is building an understanding of place values and how numbers are represented. One common mistake made when explaining math thinking is the idea of ‘carrying the one’ when adding. For example, 23+18 can be explained (especially if the equation is stacked vertically) as “3+8 =11, write a one (in the units column) and carry a one (to the tens column).” That ‘one’ being ‘carried’ is actually a ten (not a ‘one’). The problem is actually 20+10+ ‘carried 10’.	Place value chart Base 10 model Hundreds board
Sorting	The ability to notice and organize objects that are alike or different, based on various attributes. An important pre-math skill that deepens a child’s understanding of math and its foundational aspects of groupings, systems and rules.	Reinforces a child’s ability to determine object sets and visualize ‘groups of’ (the underpinning of mathematical ideas).	Attribute buttons Attribute blocks Sorting set
Subitize	The ability to see an amount and know how many there are in that group without physically counting each individual object.	A child will see ‘groups of’ without counting by units/ones. For example, a child can often see a group of objects and know there are ‘6’ or ‘12’ without counting each item individually, by virtue of seeing groups of five.	Rekenrek
Tens Facts (or Tens Buddies)	All of the pairs of numbers that make 10: 9,1; 8,2; 7,3; 6,4; 5,5.	When a child fluently knows the Tens Buddies, they can more flexibly solve math problems. For example, if a child knows 2+8, they know 3+8, 13+8, etc. Ten is a Friendly Number – it can help us solve many unknown problems.	10-frame Rekenrek
Tens Plus Facts	The concept of 10 plus any number makes decomposing numbers easier. 10+1, 10+2, 10+3… For example, 18 is 10+8, 27 is 10+17.	Often considered the first Helper Fact. Builds on the understanding of the Base 10 system.	10-frame Rekenrek Number line

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Helpful Math Tools

Manipulatives – Physical tools that help a child to count, sort, estimate and engage in learning about the magnitude of numbers in a hands-on way.
10-frame and 20-frame – Helps establish an understanding of Tens Facts (Tens Buddies).
Tally marks – Visual representation of 5 and 10 structure.
Rekenrek – The color of the beads changes after 5 beads so that a child can subitize and relate quantities to the benchmarks of 5 and 10. Gives a visual picture of an amount using the 5 and 10 structure.
Number line – Helps to count up and count down by units/ones, and to decompose numbers (the numbers in a number).
Base 10 model – Provides a visual representation of magnitude of how ten units/ones make 10, 10 tens make 100, 10 hundreds make a thousand and so on. Helps with understanding place value.
Hundreds board – A visual, big picture way of teaching 1:1 correspondence, sequencing, place value and number patterns.
Place value chart – Easily shows the value of each digit in a number.
Clock – Great for teaching how to tell time as it is to teach fractions.
Measurement – Use centimeter cubes, inch tiles, rulers.

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Basic Concepts

Key Math Terms and Strategies

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