Mathematics and the World We Live In  Mathematics Resources

## Number and Operations

The student will identify, represent, order, and compare numbers; and estimate, compute, and solve problems.

### Category

A

N

Read and write numbers from hundred-thousands to hundredths.

A

N

Represent whole numbers to 9999.

A

N

Identify the place value of a given digit from hundred-thousands to hundredths.

Place Value Game Math Slice

A

N

Compare and order whole numbers to 9999 using the appropriate symbols (>, <, and =).

A

N

Identify fractions as parts of whole units, as parts of sets, as locations on number lines, and as divisions of whole numbers.

A

N

Generate equivalent forms of whole numbers, commonly used fractions, and decimals.

A

N

Represent numbers as both improper fractions and mixed numbers.

D

Use concrete or pictorial representations to compare and order commonly used fractions.

D

Use concrete and pictorial representations to compare decimals.

D

Use various models and equivalent forms to represent, order, and compare whole numbers and commonly used fractions and mixed numbers (e.g., number lines, base ten blocks, expanded notation, Venn diagrams, and hundreds boards).

A

N

Represent whole numbers up to 10,000 in expanded form (1,000’s + 100’s +10’s +1’s).

D

Demonstrate knowledge and understanding of grade level mathematical terms.

D

Explain the relationship between addition and subtraction.

I

Explain the relationship between multiplication and division.

I

Explain how addition, subtraction, multiplication, and division affect the size and order of numbers.

D

Estimate the results of whole-number computations.

A

N

Use estimation to select a reasonable solution to a whole number computation involving addition, subtraction, or multiplication.

A

C

Add and subtract fractions with like denominators.

A

C

Multiply efficiently and accurately with single-digit whole numbers.

D

Divide efficiently and accurately with single-digit whole numbers.

A

C

Add and subtract decimals (includes monetary units).

I

Multiply decimals (includes monetary units).

I

Select appropriate methods and tools for computing with whole numbers (e.g., mental computation, estimation, calculators, paper and pencil, guess and check).

A

C

Solve one-step real-world problems involving addition or subtraction of whole numbers and/or decimals.

A

R

Solve one-step real-world problems involving multiplication of whole numbers and/or decimals.

I

Identify missing information and/or too much information in word problems.

I

Apply logical reasoning to solve real-world problems.

D

Select the appropriate computational and operational method to solve word problems.

D

Solve story problems using whole numbers, fractions, and decimals (includes money).

Algebra

The student will analyze and use symbols to generalize patterns, use properties of operations, and analyze change in various situations.

 Generalize and extend or complete patterns involving geometric figures or numbers. A AT Extend numerical and geometric patterns. D Represent and analyze patterns and relationships using words, tables, and graphs. A AT Determine the function rule for data in a function table. A AT Apply basic function rules. A AT Solve open sentences involving addition and subtraction. A AT Solve open sentences involving multiplication and division. A AT Connect open sentences to real-world situations. I Represent the idea of a variable as an unknown quantity by using a letter or a symbol. D Demonstrate understanding that an equation is a number sentence stating that two quantities are equal. D Use the commutative, associative, zero, and identity properties for addition and multiplication. I Investigate how a change in one variable relates to a change in a second variable.

Geometry

The student will analyze and describe characteristics and properties of 2- and 3-dimensional shapes, locate and specify points on a grid, and use geometric concepts (e.g., symmetry and transformations) and reasoning to solve problems.

 D Identify, compare, and analyze attributes of two- and three-dimensional shapes. A G Identify two- or three-dimensional shapes given defining attributes. Defining attributes D Develop and use mathematical language to describe characteristics and properties of geometric figures. D Identify and draw points, lines, line segments, rays, and angles. A G Identify points, lines, and rays. I Describe the relationships between lines and the characteristics of angles (e.g., parallel, perpendicular, intersecting, right, acute, and obtuse). D Compare properties of two- and three-dimensional geometric figures. D Investigate and describe the results of subdividing and combining two-dimensional geometric figures. A G Recognize congruent geometric figures. D Identify and draw lines of symmetry for two-dimensional geometric figures. A G Identify lines of symmetry for two-dimensional geometric figures. A AT Locate and specify points in Quadrant 1 of a coordinate system. D Identify, predict, and describe the results of transformations of two-dimensional geometric figures (i.e., slides, flips, and turns). A G Identify the result of a transformation (flip or slide) that has been applied to a simple two-dimensional geometric shape. I Describe a motion that will show that two shapes are congruent. D Construct and draw two- and three-dimensional geometric figures. D Create and describe mental images of objects, patterns, and paths. I Use geometric models to solve real-world problems.

Measurement

The student will estimate and determine time, length, perimeter, area, weight, capacity, and temperature and solve real-world problems involving measurement.

 D Demonstrate understanding of the concepts of length, perimeter, area, weight, capacity, volume, time, and angle measure. D Estimate using standard units of measure. A ME Select appropriate standard units to measure length, perimeter, area, capacity, volume, weight, time, temperature, and angles. A ME Use estimation to determine if a length or volume measurement is reasonable. I Demonstrate understanding that measurements are approximations. D Demonstrate understanding of the relationships among units of length. D Explore perimeter and area using a variety of models (e.g., geoboards, graph paper). A ME Find the perimeter of rectangles. D Select and use tools to measure weight and volume in customary or metric units. A ME Measure length to the nearest 1/4 inch or nearest centimeter. A ME Tell time to the nearest minute. A ME Read temperature using Fahrenheit and Celsius thermometers. D Develop strategies for estimating the perimeters and areas (such as counting square units) of geometric figures. A ME Apply the formula for finding the area of a rectangle. A R Solve real-world problems involving addition and subtraction of measurements. A R Solve real-world problems involving elapsed time to the quarter-hour.

### Data Analysis and Probability

The student will collect, organize, analyze, interpret, and display data in tables and graphs and determine the probabilities of outcomes in simple experiments.

 I Collect data using observations, surveys, and experiments. I Understand how data-collection methods could affect the results. D Construct tables, pictographs, line graphs, and bar graphs. D Interpret simple charts, tables, pictographs, line graphs, and bar graphs. A DP Interpret data displayed in bar graphs and pictographs. A DP Connect data in tables to pictographs, line graphs, or bar graphs. I Evaluate how well various representations show the collected data. D Explore and determine measures of central tendency (i.e., mean, median, and mode). A DP Determine the median of a data set. D Make predictions from data. I Design investigations to try to answer a question. M Describe the likelihood or chance of events as certain, possible, or impossible. M Explain whether an event is likely or unlikely. A DP Determine the most likely, least likely, or equally likely outcomes in simple experiments. A DP Select all possible outcomes of a simple experiment (i.e., spinner, coin toss, number or color cube).

Kindergarten

Elementary Resources

Worksheets

Algebra I

Secondary Resources

Worksheets

Science Fair

Dynamic Curriculum

Math/Science Integration

Math Online