Kansas - Mathematics: 7th Grade

  • Curriculum Standards     Adopted: 2004

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below to go to the Gizmo Details page.

1: Number and Computation

1.1: The student demonstrates number sense for rational numbers, the irrational number pi, and simple algebraic expressions in one variable in a variety of situations.

1.1.1: knows, explains, and uses equivalent representations for rational numbers and simple algebraic expressions including integers, fractions, decimals, percents, and ratios; integer bases with whole number exponents; positive rational numbers written in scientific notation with positive integer exponents; time; and money, e.g., 253,000 is equivalent to 2.53 x 10 to the 5th power or x + 5x is equivalent to 6x.

Improper Fractions and Mixed Numbers
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Percents, Fractions and Decimals
Polling: Neighborhood

1.1.2: compares and orders rational numbers and the irrational number pi.

Comparing and Ordering Decimals
Comparing and Ordering Fractions
Comparing and Ordering Integers
Comparing and Ordering Rational Numbers
Fraction Garden (Comparing Fractions)
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1

1.1.3: explains the relative magnitude between rational numbers and between rational numbers and the irrational number pi.

Comparing and Ordering Decimals
Comparing and Ordering Fractions
Comparing and Ordering Integers
Comparing and Ordering Rational Numbers
Fraction Garden (Comparing Fractions)
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1

1.1.4: knows and explains what happens to the product or quotient when:

1.1.4.a: a whole number is multiplied or divided by a rational number greater than zero and less than one,

Dividing Fractions
Dividing Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals

1.1.4.b: a whole number is multiplied or divided by a rational number greater than one,

Dividing Fractions
Dividing Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals

1.1.4.c: a rational number (excluding zero) is multiplied or divided by zero.

Chocomatic (Multiplication, Arrays, and Area)

1.1.5: explains and determines the absolute value of rational numbers.

Comparing and Ordering Integers
Real Number Line - Activity A

1.2: The student demonstrates an understanding of the rational number system and the irrational number pi; recognizes, uses, and describes their properties; and extends these properties to algebraic expressions in one variable.

1.2.1: knows and explains the relationships between natural (counting) numbers, whole numbers, integers, and rational numbers using mathematical models, e.g., number lines or Venn diagrams.

Comparing and Ordering Integers
Improper Fractions and Mixed Numbers

1.2.2: classifies a given rational number as a member of various subsets of the rational number system, e.g., - 7 is a rational number and an integer.

Improper Fractions and Mixed Numbers
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Percents, Fractions and Decimals

1.2.3: names, uses, and describes these properties with the rational number system and demonstrates their meaning including the use of concrete objects:

1.2.3.a: commutative properties of addition and multiplication (changing the order of the numbers does not change the solution);

Chocomatic (Multiplication, Arrays, and Area)

1.2.3.c: distributive property [distributing multiplication or division over addition or subtraction, e.g., 2(4 - 1) = 2(4) - 2(1) = 8 - 2 = 6];

Chocomatic (Multiplication, Arrays, and Area)

1.2.4: uses and describes these properties with the rational number system and demonstrates their meaning including the use of concrete objects:

1.2.4.a: identity properties for addition and multiplication (additive identity - zero added to any number is equal to that number; multiplicative identity - one multiplied by any number is equal to that number);

Chocomatic (Multiplication, Arrays, and Area)

1.2.4.c: zero property of multiplication (any number multiplied by zero is zero);

Chocomatic (Multiplication, Arrays, and Area)

1.2.4.d: addition and multiplication properties of equality (adding/multiplying the same number to each side of an equation results in an equivalent equation);

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Formulas for any Variable
Solving Two-Step Equations

1.3: The student uses computational estimation with rational numbers and the irrational number pi in a variety of situations.

1.3.2: uses various estimation strategies and explains how they were used to estimate rational number quantities and the irrational number pi.

Estimating Sums and Differences

1.3.4: determines the appropriateness of an estimation strategy used and whether the estimate is greater than (overestimate) or less than (underestimate) the exact answer and its potential impact on the result.

Estimating Sums and Differences

1.4: The student models, performs, and explains computation with rational numbers, the irrational number pi, and first-degree algebraic expressions in one variable in a variety of situations.

1.4.1: computes with efficiency and accuracy using various computational methods including mental math, paper and pencil, concrete objects, and appropriate technology.

Adding Real Numbers
Dividing Fractions
Dividing Mixed Numbers
Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals

1.4.2: performs and explains these computational procedures:

1.4.2.a: adds and subtracts decimals from ten millions place through hundred thousandths place;

Sums and Differences with Decimals

1.4.2.b: multiplies and divides a four-digit number by a two-digit number using numbers from thousands place through thousandths place;

Multiplying with Decimals

1.4.2.c: multiplies and divides using numbers from thousands place through thousandths place by 10; 100; 1,000;.1;.01;.001; or single-digit multiples of each; e.g., 54.2 ÷.002 or 54.3 x 300;

Multiplying with Decimals

1.4.2.d: adds, subtracts, multiplies, and divides fractions and expresses answers in simplest form;

Adding Fractions (Fraction Tiles)
Dividing Fractions
Dividing Mixed Numbers
Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers

1.4.2.e: adds, subtracts, multiplies, and divides integers;

Adding Real Numbers
Adding and Subtracting Integers
Adding and Subtracting Integers with Chips

1.4.2.f: uses order of operations (evaluates within grouping symbols, evaluates powers to the second or third power, multiplies or divides in order from left to right, then adds or subtracts in order from left to right) using whole numbers;

Order of Operations

1.4.2.g: simplifies positive rational numbers raised to positive whole number powers;

Exponents and Power Rules

1.4.4: finds prime factors, greatest common factor, multiples, and the least common multiple.

Finding Factors with Area Models

1.4.5: finds percentages of rational numbers, e.g., 12.5% x $40.25 = n or 150% of 90 is what number? (For the purposes of assessment, percents will not be between 0 and 1.)

Percent of Change
Percents and Proportions
Polling: Neighborhood

2: Algebra

2.1: The student recognizes, describes, extends, develops, and explains the general rule of a pattern in a variety of situations.

2.1.1: identifies, states, and continues a pattern presented in various formats including numeric (list or table), algebraic (symbolic notation), visual (picture, table, or graph), verbal (oral description), kinesthetic (action), and written using these attributes:

2.1.1.a: counting numbers including perfect squares, cubes, and factors and multiples (number theory);

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

2.1.1.b: positive rational numbers including arithmetic and geometric sequences (arithmetic: sequence of numbers in which the difference of two consecutive numbers is the same, geometric: a sequence of numbers in which each succeeding term is obtained by multiplying the preceding term by the same number), e.g., 2, 1/2, 1/8, 1/32, ...

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

2.1.1.c: geometric figures;

Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

2.1.1.d: measurements;

Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

2.1.1.e: things related to daily life, e.g., tide, moon cycle, or temperature.

Finding Patterns

2.1.3: extends a pattern when given a rule of one or two simultaneous changes (addition, subtraction, multiplication, division) between consecutive terms, e.g., find the next three numbers in a pattern that starts with 3, where you double and add 1 to get the next number; the next three numbers are 7, 15, and 31.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

2.2: The student uses variables, symbols, rational numbers, and simple algebraic expressions in one variable to solve linear equations and inequalities in a variety of situations.

2.2.3: shows and explains how changes in one variable affects other variables, e.g., changes in diameter affects circumference.

Circle: Circumference and Area
Measuring Trees

2.2.5: solves:

2.2.5.a: one-step linear equations in one variable with positive rational coefficients and solutions, e.g., 7x = 28 or x + 3/ = 7 or x/3 = 5;

Modeling One-Step Equations - Activity A

2.2.5.b: two-step linear equations in one variable with counting number coefficients and constants and positive rational solutions;

Modeling and Solving Two-Step Equations
Solving Two-Step Equations

2.2.5.c: one-step linear inequalities with counting numbers and one variable, e.g., 3x > 12.

Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

2.2.7: knows the mathematical relationship between ratios, proportions, and percents and how to solve for a missing term in a proportion with positive rational number solutions and monomials, e.g., 5/6 = 2/x.

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Part:Part and Part:Whole Ratios
Polling: Neighborhood
Proportions and Common Multipliers

2.3: The student recognizes, describes, and analyzes constant and linear relationships in a variety of situations.

2.3.1: recognizes constant and linear relationships using various methods including mental math, paper and pencil, concrete objects, and graphing utilities or appropriate technology.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Function Machines 2 (Functions, Tables, and Graphs)
Linear Functions
Point-Slope Form of a Line - Activity A
Using Tables, Rules and Graphs

2.3.2: finds the values and determines the rule through two operations using a function table (input/output machine, T-table).

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Introduction to Functions
Linear Functions
Using Tables, Rules and Graphs

2.3.3: demonstrates mathematical relationships using ordered pairs in all four quadrants of a coordinate plane.

Points in the Coordinate Plane - Activity A

2.4: The student generates and uses mathematical models to represent and justify mathematical relationships found in a variety of situations.

2.4.1: knows, explains, and uses mathematical models to represent and explain mathematical concepts, procedures, and relationships. Mathematical models include:

2.4.1.a: process models (concrete objects, pictures, diagrams, number lines, hundred charts, measurement tools, multiplication arrays, division sets, or coordinate grids) to model computational procedures, algebraic relationships, and mathematical relationships and to solve equations

City Tour (Coordinates)
Modeling and Solving Two-Step Equations
Real Number Line - Activity A

2.4.1.c: fraction and mixed number models (fraction strips or pattern blocks) and decimal and money models (base ten blocks or coins) to compare, order, and represent numerical quantities;

Comparing and Ordering Decimals
Comparing and Ordering Fractions
Comparing and Ordering Rational Numbers
Fraction Garden (Comparing Fractions)
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Toy Factory (Set Models of Fractions)

2.4.1.d: factor trees to find least common multiple and greatest common factor and to model prime factorization; - place value models (place value mats, hundred charts, base ten blocks, or unifix cubes) to compare, order, and represent numerical quantities and to model computational procedures;

Finding Factors with Area Models

2.4.1.f: function tables to model numerical and algebraic relationships; - factor trees to find least common multiple and greatest common factor and to model prime factorization;

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Introduction to Functions
Linear Functions
Using Tables, Rules and Graphs

2.4.1.g: coordinate planes to model relationships between ordered pairs and linear equations; - equations and inequalities to model numerical relationships

City Tour (Coordinates)
Function Machines 2 (Functions, Tables, and Graphs)
Linear Functions
Point-Slope Form of a Line - Activity A
Points in the Coordinate Plane - Activity A
Slope-Intercept Form of a Line - Activity A
Solving Equations By Graphing Each Side
Using Tables, Rules and Graphs

2.4.1.h: two- and three-dimensional geometric models (geoboards, dot paper, nets or solids) to model perimeter, area, volume, and surface area, and properties of two- and three-dimensional; - function tables to model numerical and algebraic relationships;

Fido's Flower Bed (Perimeter and Area)
Introduction to Functions
Linear Functions
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones
Using Tables, Rules and Graphs

2.4.1.i: geometric models (spinners, targets, or number cubes), process models (coins, pictures, or diagrams), and tree diagrams to model probability; - coordinate planes to model relationships between ordered pairs and linear equations;

City Tour (Coordinates)
Permutations and Combinations
Points in the Coordinate Plane - Activity A

2.4.1.j: frequency tables, bar graphs, line graphs, circle graphs, Venn diagrams, charts, tables, single stem-and-leaf plots, scatter plots, and box-and-whisker plots to organize and display data; - two- and three-dimensional geometric models (geoboards, dot paper, nets or solids) to model perimeter, area, volume, and surface area, and properties of two- and three-dimensional;

Box-and-Whisker Plots
Elevator Operator (Line Graphs)
Fido's Flower Bed (Perimeter and Area)
Graphing Skills
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Scatter Plots - Activity A
Solving Using Trend Lines
Stem-and-Leaf Plots
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

2.4.1.k: Venn diagrams to sort data and show relationships. - geometric models (spinners, targets, or number cubes), process models (coins, pictures, or diagrams), and tree diagrams to model probability;

Permutations and Combinations
Reaction Time 1 (Graphs and Statistics)

3: Geometry

3.1: The student recognizes geometric figures and compares their properties in a variety of situations.

3.1.1: recognizes and compares properties of two- and three-dimensional figures using concrete objects, constructions, drawings, appropriate terminology, and appropriate technology.

Classifying Triangles
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Surface and Lateral Area of Prisms and Cylinders

3.1.2: classifies regular and irregular polygons having through ten sides as convex or concave.

Classifying Quadrilaterals - Activity A
Classifying Triangles
Special Quadrilaterals

3.1.3: identifies angle and side properties of triangles and quadrilaterals:

3.1.3.a: sum of the interior angles of any triangle is 180°;

Triangle Angle Sum - Activity A

3.1.3.b: sum of the interior angles of any quadrilateral is 360°;

Classifying Quadrilaterals - Activity A
Polygon Angle Sum - Activity A
Triangle Angle Sum - Activity A

3.1.3.d: rectangles have angles of 90°, sides may or may not be equal;

Special Quadrilaterals

3.1.3.e: rhombi have all sides equal in length, angles may or may not be equal;

Classifying Triangles
Special Quadrilaterals

3.1.4: identifies and describes:

3.1.4.a: the altitude and base of a rectangular prism and triangular prism,

Prisms and Cylinders - Activity A

3.1.4.b: the radius and diameter of a cylinder.

Measuring Trees

3.1.5: identifies corresponding parts of similar and congruent triangles and quadrilaterals.

Classifying Quadrilaterals - Activity A
Similar Figures - Activity A

3.1.6: uses symbols for right angle within a figure, parallel, perpendicular, and triangle to describe geometric figures.

Classifying Triangles

3.1.7: classifies triangles as:

3.1.7.a: scalene, isosceles, or equilateral;

Classifying Triangles
Isosceles and Equilateral Triangles
Triangle Angle Sum - Activity A

3.1.7.b: right, acute, obtuse, or equiangular.

Classifying Triangles
Pythagorean Theorem - Activity B
Triangle Angle Sum - Activity A

3.1.9: generates a pattern for the sum of angles for 3-, 4-, 5-, ... n-sides polygons.

Polygon Angle Sum - Activity A
Triangle Angle Sum - Activity A

3.1.10: describes the relationship between the diameter and the circumference of a circle.

Circle: Circumference and Area
Measuring Trees

3.2: The student estimates, measures, and uses measurement formulas in a variety of situations.

3.2.1: determines and uses rational number approximations (estimations) for length, width, weight, volume, temperature, time, perimeter, and area using standard and nonstandard units of measure.

Fido's Flower Bed (Perimeter and Area)

3.2.2: selects and uses measurement tools, units of measure, and level of precision appropriate for a given situation to find accurate rational number representations for length, weight, volume, temperature, time, perimeter, area, and angle measurements.

Fido's Flower Bed (Perimeter and Area)
Rectangle: Perimeter and Area

3.2.4: knows and uses perimeter and area formulas for circles, squares, rectangles, triangles, and parallelograms;

Area of Parallelograms - Activity A
Circle: Circumference and Area
Perimeter, Circumference, and Area - Activity B
Rectangle: Perimeter and Area
Special Quadrilaterals

3.2.5: finds perimeter and area of two-dimensional composite figures of circles, squares, rectangles, and triangles;

Fido's Flower Bed (Perimeter and Area)

3.2.7: finds surface area of rectangular prisms using concrete objects;

3.2.7.a: surface area of cubes,

Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

3.2.7.b: volume of rectangular prisms.

Prisms and Cylinders - Activity A

3.2.8: uses appropriate units to describe rate as a unit of measure, e.g., miles per hour.

Distance-Time Graphs

3.2.9: finds missing angle measurements in triangles and quadrilaterals.

Investigating Angle Theorems - Activity A
Isosceles and Equilateral Triangles
Polygon Angle Sum - Activity A
Triangle Angle Sum - Activity A

3.3: The student recognizes and performs transformations on two- and three- dimensional geometric figures in a variety of situations.

3.3.1: identifies, describes, and performs single and multiple transformations [reflection, rotation, translation, reduction (contraction/shrinking), enlargement (magnification/growing)] on a two-dimensional figure.

Quilting Bee (Symmetry)
Reflections
Rock Art (Transformations)
Rotations, Reflections and Translations

3.4: The student relates geometric concepts to a number line and a coordinate plane in a variety of situations.

3.4.1: finds the distance between the points on a number line by computing the absolute value of their difference.

Comparing and Ordering Integers
Real Number Line - Activity A

3.4.2: uses all four quadrants of a coordinate plane to:

3.4.2.a: identify in which quadrant or on which axis a point lies when given the coordinates of a point,

City Tour (Coordinates)
Points in the Coordinate Plane - Activity A

3.4.2.b: plot points,

City Tour (Coordinates)
Points in the Coordinate Plane - Activity A

3.4.2.c: identify points,

City Tour (Coordinates)
Points in the Coordinate Plane - Activity A

3.4.2.d: list through five ordered pairs of a given line.

City Tour (Coordinates)
Points in the Coordinate Plane - Activity A

3.4.3: uses a given linear equation with whole number coefficients and constants and a whole number solution to find the ordered pairs, organize the ordered pairs using a T-table, and plot the ordered pairs on the coordinate plane.

City Tour (Coordinates)
Defining a Line with Two Points
Point-Slope Form of a Line - Activity A
Points in the Coordinate Plane - Activity A
Slope-Intercept Form of a Line - Activity A
Standard Form of a Line

4: Data

4.1: The student applies the concepts of probability to draw conclusions, generate convincing arguments, and make predictions and decisions including the use of concrete objects in a variety of situations.

4.1.1: finds the probability of a compound event composed of two independent events in an experiment or simulation.

Compound Independent Events
Compound Independent and Dependent Events
Geometric Probability - Activity A
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

4.1.2: explains and gives examples of simple or compound events in an experiment or simulation having probability of zero or one.

Compound Independent Events
Compound Independent and Dependent Events
Geometric Probability - Activity A
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

4.1.3: uses a fraction, decimal, and percent to represent the probability of:

4.1.3.a: a simple event in an experiment or simulation;

Geometric Probability - Activity A
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

4.1.3.b: a compound event composed of two independent events in an experiment or simulation.

Compound Independent Events
Compound Independent and Dependent Events
Geometric Probability - Activity A
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

4.1.4: finds the probability of a simple event in an experiment or simulation using geometric models, e.g., Using spinners or dartboards, what is the probability of landing on 2? The answer is ¼,.25, or 25%.

Geometric Probability - Activity A
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

4.2: The student collects, organizes, displays, and explains numerical (rational numbers) and non-numerical data sets in a variety of situations with a special emphasis on measures of central tendency.

4.2.1: organizes, displays, and reads quantitative (numerical) and qualitative (non-numerical) data in a clear, organized, and accurate manner including a title, labels, categories, and rational number intervals using these data displays :

4.2.1.a: frequency tables;

Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

4.2.1.b: bar, line, and circle graphs;

Elevator Operator (Line Graphs)
Graphing Skills
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

4.2.1.c: Venn diagrams or other pictorial displays;

Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

4.2.1.d: charts and tables;

Histograms
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

4.2.1.e: stem-and-leaf plots (single);

Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Stem-and-Leaf Plots

4.2.1.f: scatter plots;

Correlation
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Scatter Plots - Activity A
Solving Using Trend Lines

4.2.1.g: box-and-whiskers plots.

Box-and-Whisker Plots
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

4.2.2: selects and justifies the choice of data collection techniques (observations, surveys, or interviews) and sampling techniques (random sampling, samples of convenience, or purposeful sampling) in a given situation.

Polling: Neighborhood
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

4.2.3: conducts experiments with sampling and describes the results.

Geometric Probability - Activity A
Probability Simulations
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Spin the Big Wheel! (Probability)

4.2.4: determines the measures of central tendency (mode, median, mean) for a rational number data set.

Describing Data Using Statistics
Line Plots
Mean, Median and Mode
Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

4.2.5: identifies and determines the range and the quartiles of a rational number data set.

Box-and-Whisker Plots
Describing Data Using Statistics
Line Plots
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

4.2.6: identifies potential outliers within a set of data by inspection rather than formal calculation, e.g., consider the data set (1, 100, 101, 120, 140, 170); the outlier is 1.

Reaction Time 2 (Graphs and Statistics)

Content correlation last revised: 5/22/2007