5.NBT.A.1 Recognize that in a multi-digit number, including decimals, a digit in any place represents ten 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.
5.NBT.A.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of ten, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of ten. Use whole-number exponents to denote powers of ten.
5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths.
5.NBT.B.7.a Use concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction and between multiplication and division.
5.NF.A Use equivalent fractions as a strategy to add and subtract fractions.
5.NF.A.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions to produce an equivalent sum or difference of fractions with like denominators.
5.NF.B Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
5.NF.B.3 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers by using visual fraction models and/or equations to represent the problem.
5.NF.B.5.b Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number, explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number, and relating the principle of fraction equivalence a/b = n×a/n×b to the effect of multiplying a/b by 1.
5.NF.B.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
5.NF.B.7.a Represent division of a unit fraction by a nonzero whole number and compute such quotients using a visual fraction model. Use the relationship between multiplication and division to explain that 1/b ÷ c = 1/bc because 1/bc × c = 1/b.
5.NF.B.7.b Represent division of a whole number by a unit fraction, and compute such quotients using a visual fraction model. Use the relationship between multiplication and division to explain that a ÷ 1/b = ab because ab × 1/b = a.
5.NF.B.7.c Solve real-world problems involving division of unit fractions by nonzero whole numbers and division of whole numbers by unit fractions by using visual fraction models and/or equations to represent the problem.
5.MD.C.5 Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume.
5.MD.C.5.a Find the volume of a right rectangular prism with whole-number edge lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base.
5.MD.C.5.b Apply the formulas V = l × w × h and V = B × h (where B stands for the area of the base) for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths, and in the context of solving real-world and mathematical problems.
5.MD.C.5.c.ii Apply this technique to solve real-world problems.
5.G.A Graph points on the coordinate plane to solve real-world and mathematical problems.
5.G.A.1 Describe and understand the key attributes of the coordinate plane.
5.G.A.1.a Use a pair of perpendicular number lines (axes) with the intersection of the lines (the origin (0,0)) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates.
5.G.A.1.b Understand that the x-coordinate, the first number in an ordered pair, indicates movement parallel to the x-axis starting at the origin; and the y-coordinate, the second number, indicates movement parallel to the y-axis starting at the origin.
5.G.A.2 Represent real-world and mathematical problems by graphing points in the first quadrant of the coordinate plane (x and y both have positive values), and interpret coordinate values of points in the context of the situation.