Math Concepts

Operations & Algebraic Thinking  

• Understanding multiplication in terms of a certain number of groups each of which has the same number of objects. e.g. 4 x 8 is 4 groups of 8 objects.   

• Understanding division as the sharing of a certain number of objects into groups of equal amounts. e.g. 24 objects shared as 4 groups of 6 can be shown as 24 ÷ 4 = 6.  

• Solving word problems by multiplying and dividing with numbers up to 100.  

• Finding the "missing" numbers in multiplication and division equations.   

 e.g. 7 x __ = 21 or 36 ÷ __ = 6  

• Knowing and using the commutative, associative, and distributive properties of multiplication. (without necessarily knowing these names)  

• Recognizing the connection between multiplication and division.   e.g. finding 48 ÷ 6 by knowing the number that 6 is multiplied by to get 48.  

• Multiplying and dividing with fluency for numbers up to 100 and, by grade's end, memorizing up to the 10x table.  

• Using addition, subtraction, multiplication, and/or division to solve two-step word problems. (whole number answers only)  

• Identifying arithmetic patterns in addition and multiplication tables. 

Number & Operations in Base Ten  

• Rounding numbers to the nearest 10 and the nearest 100.  

• Adding and subtracting with fluency with numbers less than one thousand.  

• Multiplying numbers 1 to 9 by multiples of ten. e.g. 4 x 30, 7 x 50, 5 x 90.  

 Number & Operations—Fractions 

• Understanding what numerators and denominators represent in fractions. e.g. 3/4 as being 3 parts out of a total of 4 parts where the parts are all of equal size  

• Understanding and representing how fractions can be shown on a number line.  

• Understanding and showing the concept of equivalent fractions.   e.g. 2/3 = 4/6  

Note: only fractions with denominators 2, 3, 4, 6, 8. 

Measurement & Data  

• Writing and telling time to the minute and solving problems that require adding and subtracting intervals of time.  

• Estimating and measuring the liquid volume and the mass of an object and being able to solve simple word problems with mass and volume. (using only grams, kilograms, and liters with no unit conversion required) 

• Drawing and using scaled picture and bar graphs.  

• Measuring length to the 1/4 and 1/2 inch and showing the resultant data on a line plot.  

• Understanding the concept of area for 2-dimensional figures.  

• Measuring area through counting of unit squares (using square centimeters, meters, inches, and feet as well as informal units)  

• Calculating area using multiplication and addition and finding the area of composite shapes. (only rectangles and shapes with 90 right angles)  

• Finding the perimeter of a polygon and, given a perimeter, finding the lengths of missing sides and being able to do so to solve real-world problems  

Geometry 

• Categorizing shapes, identifying common attributes of different types of shapes, and recognizing that some shapes belong to more than one category. e.g. rectangles are also quadrilaterals but not all quadrilaterals are rectangles  

• Divide shapes into equal parts and use fractions to describe these parts.