5.OA.B.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane.
5.OA.B.3.a Ability to generate and analyze patterns.
5.NBT.B.6 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. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
5.NBT.B.6.a Accurate recall of division facts and multiplication facts.
5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
5.NBT.B.7.a Ability to use concrete models and pictorial representations to perform operations with decimals to hundredths.
5.NBT.B.7.d Ability to write numerical expressions or equations to represent the problem and solution.
5.NBT.B.7.e Ability to reason and explain how the models, pictures, or strategies were used to solve the problem.
5.NF Number and Operations—Fractions
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 in such a way as to produce an equivalent sum or difference of fractions with like denominators.
5.NF.A.1.a Knowledge of understanding of addition and subtraction of fractions with like denominators and unit fractions from grade 4.
5.NF.A.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.
5.NF.A.2.a Knowledge of understanding addition and subtraction of fractions as joining and separating parts referring to the same whole.
5.NF.A.2.d Ability to explain why their answer is reasonable using benchmark fractions and fraction sense.
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, e.g., by using visual fraction models or equations to represent the problem.
5.NF.B.3.a Ability to recognize that a fraction is a representation of division.
5.NF.B.4b 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. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
5.NF.B.4b.1 Knowledge of unit fractions to multiply all fractions.
5.NF.B.5a.2 Ability to reason abstractly about the magnitude of products with fractions.
5.NF.B.5b Explaining why multiplying a given number by a fraction greater than one results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); 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 x a)/ (n x b) to the effect of multiplying (a/b) by 1.
5.NF.B.5b.1 Ability to understand the differences in results when multiplying whole numbers and when multiplying fractions. (when multiplying a fraction greater than 1, the number increases and when multiplying by a fraction less than 1, the number decreases).
5.NF.B.6.b Solve a variety of problems using multiplication of fractions. Include problems involving fraction by a whole number, fraction by a fraction, fraction by a mixed number, and mixed number by a mixed number.
5.NF.B.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients.
5.NF.B.7.a Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.
5.NF.B.7.b Dividing unit fractions by a whole number is an introductory concept in grade 5.
5.NF.B.7a.2 Ability to explain the relationship between multiplication and division of a unit fraction by a non-zero whole number.
5.NF.B.7b Interpret division of a whole number by a unit fraction, and compute such quotients.
5.NF.B.7b.1 Ability to demonstrate word problems when a whole number is divided by unit fraction and compute the quotient using visual fraction models.
5.NF.B.7b.2 Create a story context for a whole number divided by a unit fraction and compute the quotient for the problem.
5.NF.B.7c Solve real-world problems involving division of unit fractions by nonzero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem.
5.NF.B.7c.1 Knowledge of the relationship between multiplication and division.
5.MD.B.2.c Ability to apply knowledge of multiplication and division to multiply and divide fractions based on the line plot data.
5.MD.B.2.d Ability to measure objects to the nearest 1/2, 1/4 or 1/8 and display that data on a line plot. Use operations to solve problems based on the data. Or interpret data on a line plot to use operations to solve problems.
5.MD.C.3.a Ability to understand that volume introduces a third dimension to figures.
5.MD.C.3.b Ability to understand the differences in liquid volume and solid volume. Liquid volume (4.MD.A.2) fills the three dimension space of a container and takes the shape of the container. Solid volume fills the space of a three-dimensional container by packing the container with solid units.
5.MD.C.3.c Knowledge that solid units are composed of 1 unit by 1 unit by 1. It called a cubic unit and it is the standard measure for finding volume.
5.MD.C.3.d Ability to find the total volume of a solid figure by packing a solid figure with cubic inches or centimeters, without gaps or overlaps, and then counting the cubic units to find the total volume. (Does not 'fill' a container randomly with cubic units).
5.MD.C.4.b Understand that the volume of a right rectangular prism can be found by first packing the container with cubes to making rows to create layers (an array of rows and columns that pack the container without gaps or overlaps).
5.MD.C.4.c Understand that given the total volume of a right rectangular prism, be able to decompose it, understanding it can be partitioned into layers, each layer can be decomposed into rows and each row into cubes. Compare the results to other right rectangular prisms with different dimensions.
5.MD.C.4.d Conceptualize a layer as the unit that is composed of rows, each row is composed of individual units. The layers are iterated to be able to predict the number of cubes needed to fill a box when a the net of a box is given.
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.5a Find the volume of a right rectangular prism with whole- number side 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. Represent three-fold whole-number products as volumes, e.g., to represent the associative property of multiplication.
5.MD.C.5a.1 Apply multiplicative reasoning to determine volume, looking for and making use of previously learned structure for finding volume using unit cubes in iterated layers. Use multiplication to find the area of the base of the container (length and width = 1 layer) and multiply the resulting area by the number of layers (height).
5.MD.C.5a.2 Ability to understand the height of the prism tells how many layers will fit in the prism.
5.MD.C.5a.3 Ability to represent three fold whole-number product as volume to represent the associative property (Volume is a derived attribute once length is specified; it can be computed as the product of three length measurements or as the product of one area and one length.)
5.MD.C.5b Apply the formulas V =(l)(w)(h) and V = (b)(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.
5.MD.C.5b.1 Ability to apply knowledge of finding volume in previous standards to develop the formula for finding volume (length x width x height).
5.MD.C.5b.2 Ability to be given a total volume to find the dimensions of the figure.
5.MD.C.5b.3 Ability to find the volume of a figure with an unknown dimension.
5.MD.C.5c Recognize volume as additive. 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.
5.MD.C.5c.1 Ability to find the total volume of two non-overlapping right rectangular prisms by finding the volume of each right rectangular prism and adding the volumes of both.
5.MD.C.5c.2 Solve problems with two non-overlapping right rectangular prisms.
5.G.A Graph points on the coordinate plane to solve real- world and mathematical problems.
5.G.A.1 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 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates 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, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
5.G.A.1.a See the skills and knowledge that are stated in the standard.