# SBS:Math Level 06 v4

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Math Level 06 Capacity Matrices

*Resources aligned to the old Math Level 08 v3 which addresses content in the new Math Level 06 v4*

- Math Level 08 Unit - Created by Cally Holste

## Contents |

## Number Sense, Properties, and Operations

**Measurement Topic:** *MA.06.611 Quantities can be expressed and compared using ratios and rates* Capacity Matrix MA.06.611

MA.06.611.01.04 Apply the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. (CAS: 6.1.1.a) (CCSS: 6.RP.1)

MA.06.611.03.04 Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. (CAS: 6.1.1.c.i) (CCSS: 6.RP.3a)

MA.06.611.05.04 Solve unit rate problems including those involving unit pricing and constant speed. (CAS: 6.1.1.c.iii) (CCSS: 6.RP.3b)

MA.06.611.06.04 Find a percent of a quantity as a rate per 100. (CAS: 6.1.1.c.iv) (CCSS: 6.RP.3c)

MA.06.611.07.04 Solve problems involving finding the whole, given a part and the percent. (CAS: 6.1.1.c.v) (CCSS: 6.RP.3c)

MA.06.611.10.04 Use ratio reasoning to convert measurement units. (CAS: 6.1.1.c.viii) (CCSS: 6.RP.3d)

**Measurement Topic:** *MA.06.612 Formulate, represent, and use algorithms with positive rational numbers with flexibility, accuracy, and efficiency* Capacity Matrix MA.06.612

MA.06.612.03.04 Find the greatest common factor of two whole numbers less than or equal to 100. (CAS: 6.1.2.c) (CCSS: 6.NS.4)

MA.06.612.04.04 Find the least common multiple of two whole numbers less than or equal to 12. (CAS: 6.1.2.d) (CCSS: 6.NS.4)

MA.06.612.05.04 Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. (CAS: 6.1.2.e) (CCSS: 6.NS.4)

MA.06.612.07.04 Compute quotients of fractions. (CAS: 6.1.2.g) (CCSS: 6.NS.1)

MA.06.612.08.04 Solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. (CAS: 6.1.2.h) (CCSS: 6.NS.1)

**Measurement Topic:** *MA.06.613 In the real number system, rational numbers have a unique location on the number line and in space* Capacity Matrix MA.06.613

MA.06.613.01.04 Use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. (CAS: 6.1.3.a.i) (CCSS: 6.NS.5)

MA.06.613.05.04 Explain when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. (CAS: 6.1.3.b.iv) (CCSS: 6.NS.6b)

MA.06.613.09.04 Write, interpret, and explain statements of order for rational numbers in realworld contexts. (CAS: 6.1.3.c.ii) (CCSS: 6.NS.7b)

MA.06.613.10.04 Define the absolute value of a rational number as its distance from 0 on the number line and interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. (CAS: 6.1.3.c.iii) (CCSS: 6.NS.7c)

MA.06.613.11.04 Distinguish comparisons of absolute value from statements about order. (CAS: 6.1.3.c.iv) (CCSS: 6.NS.7d)

MA.06.613.12.04 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane including the use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. (CAS: 6.1.3.d) (CCSS: 6.NS.8)

## Patterns, Functions, and Algebraic Structures

**Measurement Topic:** *MA.06.621 Algebraic expressions can be used to generalize properties of arithmetic* Capacity Matrix MA.06.621

MA.06.621.01.04 Write and evaluate numerical expressions involving whole number exponents. (CAS: 6.2.1.a) (CCSS: 6.EE.1)

MA.06.621.02.03 Write expressions that record operations with numbers and with letters standing for numbers. (CAS: 6.2.1.b.i) (CCSS: 6.EE.2a)

MA.06.621.04.04 Evaluate expressions at specific values of their variables including expressions that arise from formulas used in real world problems. (CAS: 6.2.1.b.iii) (CCSS: 6.EE.2c)

MA.06.621.05.04 Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). (CAS: 6.2.1.b.iv) (CCSS: 6.EE.2c)

MA.06.621.06.04 Apply the properties of operations to generate equivalent expressions. (CAS: 6.2.1.c) (CCSS: 6.EE.3)

**Measurement Topic:** *MA.06.622 Variables are used to represent unknown quantities within equations and inequalities* Capacity Matrix MA.06.622

MA.06.622.02.04 Use substitution to determine whether a given number in a specified set makes an equation or inequality true. (CAS: 6.2.2.b) (CCSS: 6.EE.5)

MA.06.622.04.04 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. (CAS: 6.2.2.d) (CCSS: 6.EE.7)

MA.06.622.06.04 Show that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. (CAS: 6.2.2.f) (CCSS: 6.EE.8)

MA.06.622.07.04 Use variables to represent two quantities in a real-world problem that change in relationship to one another. (CAS: 6.2.2.g.i) (CCSS: 6.EE.9)

MA.06.622.09.04 Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (CAS: 6.2.2.g.iii) (CCSS: 6.EE.9)

## Data Analysis, Statistics, and Probability

**Measurement Topic:** *MA.06.631 Visual displays and summary statistics of one-variable data condense the information in data sets into usable knowledge* Capacity Matrix MA.06.631

MA.06.631.03.04 Explain that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. (CAS: 6.3.1.c) (CCSS: 6.SP.3)

MA.06.631.04.04 Display numerical data in plots on a number line, including dot plots, histograms, and box plots. (CAS: 6.3.1.d.i) (CCSS: 6.SP.4)

MA.06.631.07.04 Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. (CAS: 6.3.1.d.ii.3) (CCSS: 6.SP.5c)

MA.06.631.08.04 Relate the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. (CAS: 6.3.1.d.ii.4) (CCSS: 6.SP.5d)

## Shape, Dimension, and Geometric Relationships

**Measurement Topic:** *MA.06.641 Objects in space and their parts and attributes can be measured and analyzed* Capacity Matrix MA.06.641

MA.06.641.01.04 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes. (CAS: 6.4.1.a.i) (CCSS: 6.G.1)

MA.06.641.03.04 Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths. (CAS: 6.4.1.b.i) (CCSS: 6.G.2)

MA.06.641.05.04 Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. (CAS: 6.4.1.b.iii) (CCSS: 6.G.2)

MA.06.641.10.04 Apply techniques for finding surface area in the context of solving real-world and mathematical problems. (CAS: 6.4.1.d.iii) (CCSS: 6.G.4)