When children enter elementary school their parents know that their math skills will need to be developed. Students must learn how to count with understanding, perceiving subgroups and learning the different combinations of numbers to make five.
They also have to understand the order of operations and be able to use this knowledge in word problems.
Students need to know what a number represents and have an intuitive understanding of the relationship between numbers. This is called Number Sense.
Number Sense includes an ability to identify and use strategies for adding, subtracting, counting, and solving problems. It also involves knowing how to move between different representations of number (e.g., dots, cards, numbers). It also includes an ability to judge how reasonable an answer is and routinely estimate before calculating.
Children with strong number sense easily transition between these different representations and have a good intuition about the magnitude of numbers. This is an important foundation for later math skills, such as comparing and generating numbers, and it is especially predictive of mathematical achievement in elementary school. Students who have difficulty with Number Sense, particularly Non-symbolic Number knowledge and Symbolic Number representation, often struggle to learn new materials, achieve high scores on timed tests, or complete their homework. It can lead to frustration and a mistaken belief that they "can't do math." For these kids, it's critical that teachers focus on teaching this skill early.
The first math concepts kids learn are addition and subtraction. Kids develop these skills in small steps, typically from kindergarten to fourth grade.
Adding and subtracting prepares students for multiplication and division. They’ll begin to see these as opposites, and practice strategies to help them master both.
Students must be fluent with the addition table for single-digit numbers up to around 20 before moving on to larger numbers. This builds a foundation for understanding and enables them to quickly compute larger numbers mentally.
By the end of elementary school, kids will invent their own algorithms for adding and subtracting. They’ll be able to solve problems such as 47 - 23, decompose them into their parts, and then find solutions. They’ll also be able to use a number line to show their work and understand place value. This is essential to help them get through the more complex problems. They will also need to be familiar with regrouping.
After kids have mastered addition and subtraction, it's time to learn multiplication. This is one of the most important math skills to have because it enables children to move on to more difficult concepts, like division and long multiplication.
When teaching multiplication, it's helpful to help students understand that it's simply repeated addition. This helps build a solid conceptual understanding of the concept and avoids the frustration that typically comes from rote memorization.
Once students have a firm grasp on basic multiplication, it's time to explore patterns and learn the rules of division. Start by discussing the commutative property, which tells students that the order of numbers in a multiplication table doesn't matter (for example, 6 x 3 = 18).
Encourage kids to practice their math facts using flash cards or online tools, such as Prodigy. This will enable them to develop a strong foundation that will carry over into their academic and professional lives, from calculating monthly overhead costs to determining the area of a room for blueprints or furniture.
The next step in math is geometry, which involves identifying shapes and their dimensions. This can be a difficult subject for kids, as they need to go beyond just perceiving sameness and difference to understand defining properties. They must know that a triangle is a triangle even if it isn’t prototypical, and that different four-sided shapes can have the same characteristics as a square.
Another important concept in geometry is points, which are the beginning of a shape. Points are one-dimensional and do not have length, breadth or height. To help kids grasp this, you can have them use markers to create lines on paper and connect them to form a shape.
Children also need to learn how to solve word problems. This is a good way to get them thinking like a mathematician. This includes explaining how they figured out an answer. For example, you might ask them why 7 plus 8 equals 15. This will help them develop the logical reasoning skills that are necessary for geometry and other advanced topics.