6.NS.1.a Estimate and determine the percent represented by a given model, including percents greater than 100% and less than 1%.

6.NS.1.b Represent and determine equivalencies among decimals (through the thousandths place) and percents incorporating the use of number lines, and concrete and pictorial models.

6.NS.1.c Represent and determine equivalencies among fractions (proper or improper) and mixed numbers that have denominators that are 12 or less or factors of 100 and percents incorporating the use of number lines, and concrete and pictorial models.

6.NS.1.d Represent and determine equivalencies among decimals, percents, fractions (proper or improper), and mixed numbers that have denominators that are 12 or less or factors of 100 incorporating the use of number lines, and concrete and pictorial models.

6.NS.1.e Use multiple strategies to compare and order no more than four positive rational numbers expressed as fractions (proper or improper), mixed numbers, decimals, and percents (decimals through thousandths, fractions with denominators of 12 or less or factors of 100) with and without models. Justify solutions orally, in writing or with a model. Ordering may be in ascending or descending order.

6.NS.2.a Represent integers, including models derived from contextual situations, and identify an integer represented by a point on a number line.

6.NS.2.b Compare and order integers using a number line.

6.NS.2.c Compare integers, using mathematical symbols (<, >, =).

6.NS.2.d Identify and describe the absolute value of an integer as the distance from zero on the number line.

Checkpoint opportunity

6.NS.3.a Recognize and represent patterns with bases and exponents that are whole numbers.

6.NS.3.b Recognize and represent patterns of perfect squares not to exceed 20², by using concrete and pictorial models.

6.NS.3.c Justify if a number between 0 and 400 is a perfect square through modeling or mathematical reasoning.

6.NS.3.d Recognize and represent powers of 10 with whole number exponents by examining patterns in place value.

Checkpoint opportunity

6.CE.1.a Demonstrate/model multiplication and division of fractions (proper or improper) and mixed numbers using multiple representations.

6.CE.1.b Multiply and divide fractions (proper or improper) and mixed numbers that include denominators of 12 or less. Answers are expressed in simplest form.

6.CE.1.c Investigate and explain the effect of multiplying or dividing a fraction, whole number, or mixed number by a number between zero and one.

6.CE.1.d Estimate, determine, and justify the solution to single-step and multistep problems in context that involve addition and subtraction with fractions (proper or improper) and mixed numbers, with and without regrouping, that include like and unlike denominators of 12 or less. Answers are expressed in simplest form.

6.CE.1.e Estimate, determine, and justify the solution to single-step and multistep problems in context that involve multiplication and division with fractions (proper or improper) and mixed numbers that include denominators of 12 or less. Answers are expressed in simplest form.

Checkpoint opportunity

6.CE.2.a Demonstrate/model addition, subtraction, multiplication, and division of integers using pictorial representations or concrete manipulatives.

6.CE.2.b Add, subtract, multiply, and divide two integers.

6.CE.2.c Simplify an expression that contains absolute value bars | | and an operation with two integers and represent the result on a number line.

6.CE.2.d Estimate, determine, and justify the solution to one and two-step contextual problems, involving addition, subtraction, multiplication, and division with integers.

Checkpoint opportunity

6.MG.1.a Identify and describe chord, diameter, radius, circumference, and area of a circle.

6.MG.1.b Investigate and describe the relationship between: diameter and radius; radius and circumference; and diameter and circumference.

6.MG.1.c Develop an approximation for pi (3.14) by gathering data and comparing the circumference to the diameter of various circles, using concrete manipulatives or technological models.

6.MG.1.d Develop the formula for circumference using the relationship between diameter, radius, and pi.

6.MG.1.e Solve problems, including those in context, involving circumference and area of a circle when given the length of the diameter or radius.

6.MG.2.a Develop the formula for determining the area of parallelograms and triangles using pictorial representations and concrete manipulatives.

6.MG.2.b Solve problems, including those in context, involving the perimeter and area of triangles and parallelograms.

Checkpoint opportunity

6.MG.3.a Identify and label the axes, origin, and quadrants of a coordinate plane.

6.MG.3.b Identify and describe the location (quadrant or the axis) of a point given as an ordered pair. Ordered pairs will be limited to coordinates expressed as integers.

6.MG.3.c Graph ordered pairs in the four quadrants and on the axes of a coordinate plane. Ordered pairs will be limited to coordinates expressed as integers.

6.MG.3.d Identify ordered pairs represented by points in the four quadrants and on the axes of the coordinate plane. Ordered pairs will be limited to coordinates expressed as integers.

6.MG.3.e Relate the coordinates of a point to the distance from each axis and relate the coordinates of a single point to another point on the same horizontal or vertical line. Ordered pairs will be limited to coordinates expressed as integers.

6.MG.3.f Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to determine the length of a side joining points with the same first coordinate or the same second coordinate. Ordered pairs will be limited to coordinates expressed as integers. Apply these techniques in the context of solving contextual and mathematical problems.

Checkpoint opportunity

6.MG.4.a Identify regular polygons.

6.MG.4.b Draw lines of symmetry to divide regular polygons into two congruent parts.

6.MG.4.c Determine the congruence of segments, angles, and polygons given their properties.

6.MG.4.d Determine whether polygons are congruent or noncongruent according to the measures of their sides and angles.

6.PS.1.a Formulate questions that require the collection or acquisition of data with a focus on circle graphs.

6.PS.1.b Determine the data needed to answer a formulated question and collect the data (or acquire existing data) using various methods.

6.PS.1.c Determine the factors that will ensure that the data collected is a sample that is representative of a larger population.

6.PS.1.d Organize and represent data using circle graphs, with and without the use of technology tools. The number of data values should be limited to allow for comparisons that have denominators of 12 or less or those that are factors of 100.

6.PS.1.e Analyze data represented in a circle graph by making observations and drawing conclusions.

6.PS.1.f Compare data represented in a circle graph with the same data represented in other graphs, including but not limited to bar graphs, pictographs, and line plots (dot plots), and justify which graphical representation best represents the data.

6.PS.2.a Represent the mean of a set of data graphically as the balance point represented in a line plot (dot plot).

6.PS.2.b Determine the effect on measures of center when a single value of a data set is added, removed, or changed.

6.PS.2.c Observe patterns in data to identify outliers and determine their effect on mean, median, mode, or range.

6.PFA.1.a Represent a relationship between two quantities using ratios.

6.PFA.1.b Represent a relationship in context that makes a comparison by using the notations ^a/_b, a:b, and a to b.

6.PFA.1.c Represent different comparisons within the same quantity or between different quantities.

6.PFA.1.d Create a relationship in words for a given ratio expressed symbolically.

6.PFA.1.e Create a table of equivalent ratios to represent a proportional relationship between two quantities, when given a ratio.

6.PFA.1.f Create a table of equivalent ratios to represent a proportional relationship between two quantities, when given a contextual situation.

6.PFA.2.a Identify the unit rate of a proportional relationship represented by a table of values, a contextual situation, or a graph.

6.PFA.2.b Determine a missing value in a ratio table that represents a proportional relationship between two quantities using a unit rate.

6.PFA.2.c Determine whether a proportional relationship exists between two quantities, when given a table of values, context, or graph.

6.PFA.2.d When given a contextual situation representing a proportional relationship, find the unit rate and create a table of values or a graph.

6.PFA.2.e Make connections between and among multiple representations of the same proportional relationship using verbal descriptions, ratio tables, and graphs.

Checkpoint opportunity