1: Number and Computation

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

1.1.1: knows, explains, and uses equivalent representations for rational numbers expressed as fractions, terminating decimals, and percents; positive rational number bases with whole number exponents; time; and money.

Part-to-part and Part-to-whole Ratios

1.1.2: compares and orders:

1.1.2.a: integers;

Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

1.1.2.b: fractions greater than or equal to zero,

Adding Fractions (Fraction Tiles)
Fraction Artist 2 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)
Modeling Fractions (Area Models)
Rational Numbers, Opposites, and Absolute Values
Toy Factory (Set Models of Fractions)

1.1.2.c: decimals greater than or equal to zero through thousandths place.

Adding Whole Numbers and Decimals (Base-10 Blocks)
Comparing and Ordering Decimals
Modeling Decimals (Area and Grid Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Treasure Hunter (Decimals on the Number Line)

1.1.3: explains the relative magnitude between whole numbers, fractions greater than or equal to zero, and decimals greater than or equal to zero.

Comparing and Ordering Decimals
Fraction Garden (Comparing Fractions)
Modeling Decimals (Area and Grid Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Rational Numbers, Opposites, and Absolute Values
Treasure Hunter (Decimals on the Number Line)

1.1.4: knows and explains numerical relationships between percents, decimals, and fractions between 0 and 1, e.g., recognizing that percent means out of a 100, so 60% means 60 out of 100, 60% as a decimal is .60, and 60% as a fraction is 60/100.

Modeling Decimals (Area and Grid Models)
Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals

1.1.5: uses equivalent representations for the same simple algebraic expression with understood coefficients of 1, e.g., when students are developing their own formula for the perimeter of a square, they combine s + s + s + s to make 4s.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

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.

1.2.2: identifies prime and composite numbers and explains their meaning.

Chocomatic (Multiplication, Arrays, and Area)
Factor Trees (Factoring Numbers)
Finding Factors with Area Models

1.2.3: 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 and associative properties of addition and multiplication (commutative - changing the order of the numbers does not change the solution; associative - changing the grouping of the numbers does not change the solution);

Adding and Subtracting Integers
Adding on the Number Line
Equivalent Algebraic Expressions I

1.2.3.i: additive inverse property (every number has a value known as its additive inverse and when the original number is added to that additive inverse, the answer is zero), e.g., +5 + (-5) = 0.

Adding and Subtracting Integers

1.2.4: recognizes and explains the need for integers, e.g., with temperature, below zero is negative and above zero is positive; in finances, money in your pocket is positive and money owed someone is negative.

Adding on the Number Line
Integers, Opposites, and Absolute Values

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 or the irrational number pi.

Estimating Sums and Differences

1.4: The student models, performs, and explains computation with positive rational numbers and integers 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.

Estimating Sums and Differences
Improper Fractions and Mixed Numbers
Sums and Differences with Decimals

1.4.2: performs and explains these computational procedures:

1.4.2.b: adds and subtracts decimals from millions place through thousandths place;

Adding Whole Numbers and Decimals (Base-10 Blocks)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Sums and Differences with Decimals

1.4.2.f: adds, subtracts, and multiplies fractions (including mixed numbers) expressing answers in simplest form; e.g., 5 1/4 x 1/3 = 21/4 x 1/3 = 7/4 or 1 3/4

Fractions with Unlike Denominators

1.4.2.g: finds the root of perfect whole number squares;

Square Roots

1.4.2.h: uses basic order of operations (multiplication and division in order from left to right, then addition and subtraction in order from left to right) with whole numbers;

Order of Operations

1.4.4: identifies, explains, and finds the prime factorization of whole numbers

Factor Trees (Factoring Numbers)
Finding Factors with Area Models

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

Finding Factors with Area Models

1.4.6: finds a whole number percent (between 0 and 100) of a whole number, e.g., 12% of 40 is what number?

Percent of Change
Percents and Proportions

2: Algebra

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

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

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

Arithmetic and Geometric Sequences
Chocomatic (Multiplication, Arrays, and Area)
Finding Patterns
Function Machines 1 (Functions and Tables)
Square Roots

2.1.1.e: things related to daily life, e.g., time (a full moon every 28 days), tide, calendar, traffic, or appropriate topics across the curriculum.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

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

2.2.1: explains and uses variables and/or symbols to represent unknown quantities and variable relationships, e.g., x < 2.

Square Roots
Using Algebraic Expressions

2.2.2: uses equivalent representations for the same simple algebraic expression with understood coefficients of 1, e.g., when students are developing their own formula for the perimeter of a square they combine s + s + s + s to make 4s.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

2.2.3: solves:

2.2.3.a: one-step linear equations (addition, subtraction, multiplication, division) with one variable and whole number solutions, e.g., 2x = 8 or x + 7 = 12

Solving Equations on the Number Line

2.2.4: explains and uses equality and inequality symbols (=, not equal, <, less than or equal to, >, greater than or equal to) and corresponding meanings (is equal to, is not equal to, is less than, is less than or equal to, is greater than, is greater than or equal to) to represent mathematical relationships with positive rational numbers.

Comparing and Ordering Decimals
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

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

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

Arithmetic Sequences
Compound Interest
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Slope-Intercept Form of a Line

2.3.2: finds the values and determines the rule with one operation 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
Points, Lines, and Equations

2.3.3: generalizes numerical patterns up to two operations by stating the rule using words, e.g., If the sequence is 2400, 1200, 600, 300, 150, ..., what is the rule? In words, the rule could be split the number in half or divide the number before by 2.

Function Machines 1 (Functions and Tables)

2.3.4: uses a given function table (input/output machine, T-table) to identify, plot, and label the ordered pairs using the four quadrants of a coordinate plane.

Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Points, Lines, and Equations

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

2.4.1: knows, explains, and uses mathematical models to represent 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 planes/grids) to model computational procedures and mathematical relationships and to solve equations

Comparing and Ordering Decimals
Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)
Integers, Opposites, and Absolute Values
Modeling Fractions (Area Models)
Rational Numbers, Opposites, and Absolute Values
Toy Factory (Set Models of Fractions)
Treasure Hunter (Decimals on the Number Line)

2.4.1.b: 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;

Comparing and Ordering Decimals
Modeling Whole Numbers and Decimals (Base-10 Blocks)

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;

Adding Fractions (Fraction Tiles)
Adding Whole Numbers and Decimals (Base-10 Blocks)
Comparing and Ordering Decimals
Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)
Modeling Decimals (Area and Grid Models)
Modeling Fractions (Area Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Toy Factory (Set Models of Fractions)
Treasure Hunter (Decimals on the Number Line)

2.4.1.d: factor trees to find least common multiple and greatest common factor

Finding Factors with Area Models

2.4.1.e: equations and inequalities to model numerical relationships

Comparing and Ordering Decimals

2.4.1.f: function tables (input/output machines, T-tables) to model numerical and algebraic relationships;

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Points, Lines, and Equations

2.4.1.g: two-dimensional geometric models (geoboards or dot paper) to model perimeter, area, and properties of geometric shapes and three-dimensional geometric models (nets or solids) and real-world objects to model volume and to identify attributes (faces, edges, vertices, bases) of geometric shapes;

Fido's Flower Bed (Perimeter and Area)
Perimeter and Area of Rectangles

2.4.1.h: tree diagrams to organize attributes and determine the number of possible combinations;

Permutations and Combinations

j.: frequency tables, bar graphs, line graphs, circle graphs, Venn diagrams, line plots, charts, tables, single stem-and-leaf plots, and scatter plots to organize and display data;

Distance-Time Graphs
Graphing Skills
Histograms
Mascot Election (Pictographs and Bar Graphs)
Mean, Median, and Mode
Prairie Ecosystem
Reaction Time 1 (Graphs and Statistics)
Stem-and-Leaf Plots

3: Geometry

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

3.1.3: names and describes the solids [prisms (rectangular and triangular), cylinders, cones, spheres, and pyramids (rectangular and triangular)] using the terms faces, edges, vertices, and bases.

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

3.1.4: recognizes all existing lines of symmetry in two-dimensional figures.

Quilting Bee (Symmetry)

3.1.6: recognizes and uses symbols for angle (find symbol for), line(<--->), line segment (---), ray (-->), parallel (||), and perpendicular (|_).

Elevator Operator (Line Graphs)

3.1.9: recognize that the sum of the angles of a triangle equals 180°.

Isosceles and Equilateral Triangles
Polygon Angle Sum
Triangle Angle Sum

3.1.10: determines the radius or diameter of a circle given one or the other.

Circles

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

3.2.1: determines and uses whole 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, explains the selection of, 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.

Area of Triangles
Beam to Moon (Ratios and Proportions)
Fido's Flower Bed (Perimeter and Area)
Measuring Trees

3.2.3: converts:

3.2.3.a: within the customary system, e.g., converting feet to inches, inches to feet, gallons to pints, pints to gallons, ounces to pounds, or pounds to ounces;

Unit Conversions

3.2.3.b: within the metric system, e.g., converting millimeters to meters, meters to millimeters, liters to kiloliters, kiloliters to liters, milligrams to grams, or grams to milligrams

Unit Conversions

3.2.5: recognizes and states perimeter and area formulas for squares, rectangles, and triangles.

3.2.5.a: uses given measurement formulas to find perimeter and area of: squares and rectangles,

Area of Parallelograms
Area of Triangles
Chocomatic (Multiplication, Arrays, and Area)
Fido's Flower Bed (Perimeter and Area)
Perimeter and Area of Rectangles

3.2.5.b: figures derived from squares and/or rectangles.

Area of Parallelograms
Area of Triangles

3.2.7: finds the volume of rectangular prisms using concrete objects.

Balancing Blocks (Volume)

3.2.8: estimates an approximate value of the irrational number pi.

Circumference and Area of Circles

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 one or two transformations (reflection, rotation, translation) on a two-dimensional figure.

Circles
Holiday Snowflake Designer
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: uses a number line (horizontal/vertical) to order integers and positive rational numbers (in both fractional and decimal form).

Comparing and Ordering Decimals
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

3.4.2: organizes integer data using a T-table and plots the ordered pairs in all four quadrants of a coordinate plane (coordinate grid).

Function Machines 2 (Functions, Tables, and Graphs)
Slope

3.4.3: uses all four quadrants of the coordinate plane to:

3.4.3.a: identify ordered pairs of integer values on a given graph;

City Tour (Coordinates)
Elevator Operator (Line Graphs)
Points in the Coordinate Plane
Points, Lines, and Equations

3.4.3.b: graph ordered pairs of integer values.

City Tour (Coordinates)
Elevator Operator (Line Graphs)
Function Machines 2 (Functions, Tables, and Graphs)
Points in the Coordinate Plane
Points, Lines, and Equations
Slope

4: Data

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

4.1.1: recognizes that all probabilities range from zero (impossible) through one (certain) and can be written as a fraction, decimal, or a percent, e.g., when you flip a coin, the probability of the coin landing on heads (or tails) is 1/5,.5, or 50%. The probability of flipping a head on a two-headed coin? The probability of flipping a tail on a two-headed coin?

Geometric Probability
Independent and Dependent Events
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

4.1.2: lists all possible outcomes of an experiment or simulation with a compound event composed of two independent events in a clear and organized way, e.g., Using a tree diagram or list to find all the possible color combinations of pant and shirt ensembles, if there are 3 shirts (red, green, blue) and 2 pairs of pants (black and brown).

Permutations and Combinations

4.1.3: recognizes whether an outcome in a compound event in an experiment or simulation is impossible, certain, likely, unlikely, or equally likely.

Independent and Dependent Events
Theoretical and Experimental Probability

4.1.4: represents the probability of a simple event in an experiment or simulation using fractions and decimals, e.g., The probability of rolling an even number on a single number cube is represented by ½ or .5.

Independent and Dependent Events
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.b: frequency tables and line plots;

Histograms
Mascot Election (Pictographs and Bar Graphs)
Mean, Median, and Mode
Reaction Time 2 (Graphs and Statistics)
Stem-and-Leaf Plots

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

Elevator Operator (Line Graphs)
Graphing Skills
Mascot Election (Pictographs and Bar Graphs)
Reaction Time 1 (Graphs and Statistics)

4.2.1.e: charts and tables;

Stem-and-Leaf Plots

4.2.1.f: single stem-and-leaf plots;

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

4.2.1.g: scatter plots;

Graphing Skills
Trends in Scatter Plots

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.

Populations and Samples
Reaction Time 2 (Graphs and Statistics)

4.2.3: uses sampling to collect data and describe the results.

Describing Data Using Statistics
Polling: City
Populations and Samples
Reaction Time 2 (Graphs and Statistics)

4.2.4: determines mean, median, mode, and range for:

4.2.4.a: a whole number data set,

Box-and-Whisker Plots
Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Stem-and-Leaf Plots