Number and Operations
Early Grades (K–2):
Counting: Being able to count from 1-20 and to count objects up to 20.
Cardinality: The ability to not just be able to count, but also understand the value or amount they counted and to understand the relationship of numbers.
Base-Ten: Understanding place values of numbers. For example: 14 has 1 ten and 4 ones.
Early fraction concepts: The ability to understand that a single object can be divided into equal parts.
These four concepts build the foundational blocks of number sense to help students learn and understand higher concepts in math.
Resources:
Subitizing—the ability to instantly recognize the number of objects in a set without counting—is a crucial early math skill. You can keep this skill sharp over the summer with free, screen-free, and low-prep activities that turn everyday household items and outdoor play into engaging, conceptual math practice. Subitizing can be connected to number value, number relationships, ten frames, adding, subtracting, multiplying, dividing, and fractions. If you are still not sure what subitizing is think about a domino that has dots on two sides. Children begin to recognize patterns like 5 has 4 dots and 1 dot or 3 dots and 2 dots. The beginning of addition.
Subitizing Activities:
Dominoes
https://littlemindsatwork.org/freebies/math-numbers-free-download-dominoes
Have your child sort and subitize toys
Play card games like Go Fish, they have to use the suit shapes and identify the number. Older students can play Uno, Crazy Eight, or Solitaire.
Children can subitize anything from toys, food, petals, animals, cars, or colors.
Adding and Subtracting
Beginning addition starts with adding two single digit numbers like 5 and 3 is 8. Then it moves to 2 digit to 1 digit like 10 and 5 is 15 and then more complex like 12 and 3. The numbers get more complex has they move towards third grade. Subtracting seems harder for some children, which is why subitizing is so important. For example, going back to the domino with 3 dots on one side and 2 dots on the other. Students can begin to understand that 3 and 2 are 5, so they can also connect that 5 take away 3 is 2 and vice versa with these visuals. The most important concept though is that the children understand the relation between numbers. For example 10 can be made from 1 and 9, 7 and 3, and 6 and 4.
Use cards that are 1 through 9 and play make ten.
Create ten frames using egg cartons, popcycle sticks, card stock, sticks from outside, or cardboard boxes. Ten frames are two groups of five. They can use them for adding and subtracting.
Middle & Upper Grades (3–8):
Advanced whole number operations: This adding, subtracting, multiplying, and dividing numbers in the tens, hundreds, thousands and up.
Decimals: Decimals are introduced in first and second in the form of money and in fourth as an extension of fractions. They learn that deciamls are parts of a whole and measurements like centameters.
Operations with fractions: After K-2, students move from understanding that a whole can be separated into equal parts to learning about what a fraction is to comparing fractions, adding, subtracting, multiplying, and dividing them.
Resources:
Multiplying/Division:
https://www.gettingsmart.com/2017/06/03/5-free-multiplication-apps/
https://researchparent.com/learn/mathematics/multiplication-and-division/
https://www.education.com/resources/math/multiplication/multiplication-fact-fluency/
https://www.coolmathgames.com/c/multiplication-division-games
Decimals/Fractions: