Common Core Math Standards
- We are learning to make sense of problems and persevere in solving them.
- We are learning to reason abstractly and quantitatively.
- We are learning to make viable arguments and critique the reasoning of others.
- We are learning to model with mathematics.
- We are learning to use appropriate tools strategically.
- We are learning to attend to precision.
- We are learning to look for and make use of structure.
- We are learning to look for and express regularity in repeated reasoning.
- We are learning to use parentheses, brackets, or braces in numerical expressions, and to evaluate expressions with these symbols.
- We are learning to write simple expressions that record calculations with numbers. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 x (8 + 7).
- We are learning to form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. We are learning to identify apparent relationships between corresponding terms. Example follows. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence.
- We are learning that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
- When multiplying a number by powers of 10 (for example, 10, 100) we can explain patterns in the number of zeros of the product. We can explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10.
- We are learning to use whole-number exponents to denote powers of 10.
- We are learning to read and write decimals to thousandths using base-ten numerals, number names, and expanded form, for example, 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000).
- We are learning to compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
- We are learning to use place value understanding to round decimals to any place.
- We are learning to fluently multiply multi-digit whole numbers using the standard algorithm.
- We are learning to find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.
- We are learning to illustrate and explain our calculation by using equations, rectangular arrays, and/or area models.
- We are learning to add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings.
- We are learning various ways to add, subtract, multiply, and divide decimals to hundredths based on place value, properties of operations, and/or the relationship between addition and subtraction. We can relate the strategy to a written method and explain the reasoning used.
- We are learning to add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Example follows. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)
- We are learning to solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, for example, by using visual fraction models or equations to represent the problem.
- We are learning to use benchmark fractions and our number sense of fractions to estimate mentally and assess the reasonableness of answers. Example follows. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < Ω.
- We are learning to interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b)
- We are learning to solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, for example, by using visual fraction models or equations to represent the problem. Example follows on next two charts. For example, interpret æ as the result of dividing 3 by 4, noting that æ multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size æ.
- We are learning to interpret the product (a/b) x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q ÷ b. Example follows on next chart. For example, use a visual fraction model to show (2/3) x 4 = 8/3, and create a story context for this equation. Do the same with (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) = ac/bd.)
- We are learning to find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths.
- We are learning to multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
- We are learning to interpret multiplication as scaling (resizing), by comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
- We are learning to interpret multiplication as scaling (resizing), by explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case).
- We are learning to interpret multiplication as scaling (resizing), by explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number.
- We are learning to interpret multiplication as scaling (resizing), by relating the principle of fraction equivalence a/b = (n x a)/(n x b) to the effect of multiplying a/b by 1.
- We are learning to solve real world problems involving multiplication of fractions and mixed numbers, for example, by using visual fraction models or equations to represent the problem.
- We are learning to apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
- We are learning to interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) x 4 = 1/3.
- We are learning to interpret division of a whole number by a unit fraction, and compute such quotients. For example, use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 x (1/5) = 4.
- We are learning to solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, for example, by using visual fraction models and equations to represent the problem. Example follows. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally?
- We are learning to convert among different-sized standard measurement units within a given measurement system (for example, convert 5 cm to 0.05 m). We are learning to use these conversions in solving multi-step, real world problems.
- We are learning to make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8).
- We are learning to use operations on fractions to solve problems involving information presented in line plots.
- We are learning that a cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume.
- We know that a solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.
- We are learning to measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
- We are learning to relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
- We are learning to find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes. We are learning that the volume is the same as would be found by multiplying the edge lengths, or equivalently by multiplying the height by the area of the base.
- We are learning to represent threefold whole-number products as volumes, for
- We are learning to apply the formulas V = l x w x h and V = b x h for rectangular prisms to find volumes of right rectangular prisms with whole number edge lengths in the context of solving real world and mathematical problems.
- We are learning to find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.
- We are learning to recognize volume as additive.
- We are learning to use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the zero on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates.
- We understand that the first number of a graph point on the coordinate plane shows how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis.
- We are learning the convention that the names of the two axes and the coordinates correspond (for example, x-axis and x-coordinate, y-axis and y-coordinate).
- We are learning to represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane. We are learning to interpret coordinate values of points in the context of the situation.
- We understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.
- We are learning to classify two-dimensional figures in a hierarchy based on properties.