Represent a fraction $(\frac{a}{b})$ on a number line by marking off a lengths of size $(\frac{1}{b})$ from zero.
Explain equivalence and compare fractions by reasoning about their size using visual fraction models and number lines.
Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers.
Compare two fractions with the same numerator or with the same denominator by reasoning about their size (recognizing that fractions must refer to the same whole for the comparison to be valid). Record comparisons using < , >, or = and justify conclusions.
For a given or collected set of data, create a scaled (one-to-many) picture graph and scaled bar graph to represent a data set with several categories.
Determine a simple probability from a context that includes a picture.
Solve one- and two-step how many more“ and “how many less” problems using information presented in scaled graphs.“
Measure lengths using rulers marked with halves and fourths of an inch to generate data and create a line plot marked off in appropriate units to display the data.
Tell and write time to the nearest minute; measure time intervals in minutes (within 90 minutes.)
Solve real-world problems involving addition and subtraction of time intervals in minutes by representing the problem on a number line diagram.
Estimate and measure liquid volumes and masses of objects using liters (l), grams (g), and kilograms (kg).
Use the four operations to solve one-step word problems involving masses or volumes given in the same metric units.
Find the area of a rectangle with whole number side lengths by tiling without gaps or overlays and counting unit squares.
Count unit squares (square cm, square m, square in, square ft, and improvised or non-standard units) to determine area.
Relate area to the operations of multiplication using real-world problems, concrete materials, mathematical reasoning, and the distributive property.
Decompose rectilinear figures into smaller rectangles to find the area, using concrete materials.
Construct rectangles with the same perimeter and different areas or the same area and different perimeters.
Solve real-world problems involving perimeters of polygons, including finding the perimeter given the side lengths and finding an unknown side length of rectangles.
Recognize and describe polygons (up to 8 sides), triangles, and quadrilaterals (rhombuses, rectangles, and squares) based on the number of sides and the presence or absence of square corners.
Draw examples of quadrilaterals that are and are not rhombuses, rectangles, and squares.
Interpret and write equations for multiplicative comparisons.
Solve word problems involving multiplicative comparison using drawings and write equations to represent the problem, using a symbol for the unknown number.
Determine and justify solutions for multi-step word problems, including problems where remainders must be interpreted.
Write equations to show solutions for multi-step word problems with a letter standing for the unknown quantity.
Determine reasonableness of answers for multi-step word problems, using mental computation and estimation strategies including rounding.
For whole numbers in the range 1 to 100, find all factor pairs, identifying a number as a multiple of each of its factors.
Determine whether a whole number in the range 1 to 100 is a multiple of a given one-digit number.
Determine whether a whole number in the range 1 to 100 is prime or composite.
Generate and analyze a number or shape pattern that follows a given rule.
Using models and quantitative reasoning, explain that in a multi-digit whole number, a digit in any place represents ten times what it represents in the place to its right.
Read and write multi-digit whole numbers using standard form, word form, and expanded form.
Use place value understanding to compare two multi-digit numbers using >, =, and < symbols.
Round multi-digit whole numbers to any place using place value understanding.
Use place value strategies to fluently add and subtract multi-digit whole numbers and connect strategies to the standard algorithm.
Find the product of two factors (up to four digits by a one-digit number and two two-digit numbers), using strategies based on place value and the properties of operations.
