Whole Numbers and Sets

• Skip count by different increments.
• Recognize, read aloud, and write the numerals in order from zero to one million.
• Understand and identify place value for each digit in numbers to the trillions place.
• Apply expanded notation to model place value through the trillions place.
• Represent numbers on a number line.
• Identify the factors of a number.
• Identify the value of Roman numerals.
• Identify even and odd numbers.
• Identify a number that comes after a given number.
• Identify a number that comes before a given number.
• Identify a number that comes between two given numbers.
• Identify one, ten, one hundred, and one thousand more than a given number.
• Round numbers to the nearest ten, hundred, and thousand.
• Write numbers in expanded and word form.
• Estimate sums and differences up to 100.
• Continue to develop the ability to understand and use ordinal numbers.
• Apply ordinals to daily experiences.
• Use comparison symbols (<, =, >).
• Arrange three-digit numerals from least to greatest.
• Use a calculator to add, subtract, multiply, and divide sets.
• Multiply and divide by powers of ten using mental math.

Patterns and Operations: Algebraic Thinking

• Review addition and subtraction facts 0-20.
• Learn multiplication facts 0-12.
• Learn division facts 1-12.
• Identify fact families.
• Identify a missing addend.
• Use manipulatives to model and solve multiplication and division problems.
• Understand that addition and subtraction are inverse operations.
• Understand that multiplication and division are inverse operations.
• Use inverse relationships between operations to check answers.
• Copy, extend, describe, and create simple repetitive patterns.
• Identify a missing symbol in a repeating pattern.
• Identify a missing number in a sequence.
• Use variables in contextual situations.
• Use inverse relationships to solve for a variable in an equation.
• Solve a multi-step equation for a given variable.
• Write an equation to represent a model.
• Identify and write a function rule.
• Write dictated equations.
• Add five single-digit addends without and with regrouping.
• Add, subtract, multiply, and divide multi-digit numbers.
• Use addition, subtraction, multiplication, and division to solve one- and two-step word problems.
• Recognize and apply the Associative Property of Addition.
• Recognize and apply the Associative Property of Multiplication.
• Recognize and apply the Commutative Property of Addition.
• Recognize and apply the Commutative Property of Multiplication.
• Recognize and apply the Identity Property of Multiplication.
• Recognize and apply the Zero Property of Multiplication.
• Apply the Distributive Property.
• Use the Distributive Property to solve for a variable.
• Recall the order of operations in math.
• Understand the absolute value of a number.
• Read, write, and simplify an exponential expression.
• Apply computational thinking to design an algorithm and to solve problems.
• Use models and simulation to explore complex problems.

Geometry

• Understand geometric terms.
• Identify, name, and describe polygons.
• Identify angles, vertices, and sides.
• Identify and label a line, segment, and ray.
• Identify, name, and describe solids.
• Identify the interior and the exterior of a shape.
• Differentiate between regular and irregular polygons.
• Calculate the area of a regular and an irregular shape.
• Calculate the perimeter of a regular and an irregular shape.
• Find the volume of a solid.
• Demonstrate the knowledge of parallel, perpendicular, and oblique lines and line segments.
• Identify and draw congruent shapes, lines, or line segments.
• Identify and draw horizontal and vertical line segments.
• Identify and draw parallel and perpendicular line segments.
• Identify the diameter, radius, and circumference of a circle.
• Use a formula to calculate circumference.
• Construct and name angles: acute, obtuse, and right.
• Use a protractor to draw angles of a given degree.
• Combine geometric shapes to make new shapes.
• Sort shapes and explain the sorting rule.
• Classify objects according to color, shape, size, function, likeness, and differences.
• Identify and draw a horizontal and vertical line of symmetry.
• Identify similar shapes.
• Classify triangles and quadrilaterals.
• Create symmetrical designs.
• Create patterns.
• Draw a reflection over a line of symmetry.
• Use a geometric net to make a model of a solid shape.
• Use a geoboard to model polygons and angles.
• Use geometric shapes to build a model.
• Identify how geometry affects bridge design and function, and apply that knowledge to the design and construction of a bridge.
• Create tessellations.
• Perform transformations: translation, rotation, reflection.

Measurement and Estimation

• Use a ruler to measure inches, feet, yards, and centimeters.
• Draw line segments to the nearest 1/4 inch.
• Draw line segments to the nearest millimeter.
• Use a ruler to draw shapes according to given measurements.
• Order objects by length or height.
• Use digital and analog clocks to tell, write, and show time to the nearest minute.
• Order events by time.
• Calculate elapsed time.
• Compare events according to duration.
• Solve problems using a calendar.
• Write a date in word and digital form.
• Represent numbers on a number line.
• Read a Fahrenheit thermometer.
• Identify units of capacity: cup, pint, quart, gallon, milliliter, liter, teaspoon, and tablespoon.
• Make direct comparisons using measurable attributes such as length, weight, and capacity.
• Understand that one task may take more or less time to accomplish than another task. Make an estimate and experiment to test the estimate.
• Understand that one item may weigh more or less than another item. Make an estimate and experiment to test the estimate.
• Understand that one item may hold more or less than another item. Make an estimate and experiment to test the estimate.
• Calculate equivalent measurements.
• Convert measurements.
• Draw a diagram to scale.
• Recognize a scale factor.
• Use a map scale and a ruler to determine the distance between locations.
• Use a map scale to convert inches to miles.
• Round decimal numbers to the nearest thousandth.

Reasoning, Problem Solving, and Communication

• Make a prediction and draw conclusions based on evidence.
• Use simple logic to solve a problem.
• Use simple logic to solve a mathematical word problem.
• Use simple logic to develop a strategy.
• Describe how a problem was solved.
• Determine whether a solution to a problem is reasonable.
• Identify the questions asked in a problem.
• Recognize when additional information is required to solve a problem.
• Use the correct mathematical process to solve a problem.
• Develop a simple understanding of an algorithm using computer-free exercises.
• Write an algorithm to complete a specific task.
• Apply computational thinking to design an algorithm and to solve problems.
• Develop an understanding of four key techniques to computational thinking: decomposition, pattern recognition, abstraction, and algorithms.
• Use models and simulation to explore complex problems.
• Read and write code.
• Draw an object using pixels.
• Examine connections between elements of mathematics and computer science including binary numbers, logic, sets, and functions.

Money

• Identify pennies, nickels, dimes, quarters, and dollar bills.
• Find the value of a set of coins.
• Compare monetary amounts using an inequality symbol.
• Select coins for a given amount.
• Pay for items and make change using coins and bills.
• Add, subtract, multiply, and divide money amounts using a decimal to represent the monetary values.
• Compare monetary values and determine if one set is equal to, greater than, or less than the other set.
• Write money as a fraction of a dollar and with a dollar sign and decimal point.
• Solve word problems using money.
• Understand that money is accepted as final payment for goods and services.
• Identify the person on United States currency.
• Learn about banks.
• Write a check.
• Analyze a cost and benefits chart.
• Calculate the profit on goods.
• Determine an equilibrium price.
• Make a business plan and budget.
• Plan a family vacation, and stay within a total budget.

Fractions

• Make models that represent given fractions.
• Recognize fractional parts of a given whole.
• Draw pictures to represent fractions.
• Write a fraction to represent a part of a whole.
• Identify a fraction of a shape.
• Compare fractions with like and unlike denominators.
• Identify equivalent fractions.
• Expand a fraction to find equivalent fractions.
• Write fractions in numeral and word form.
• Locate rational numbers on a number line.
• Use number lines to add fractions with like denominators.
• Reduce a fraction to lowest terms.
• Identify numerator and denominator.
• Represent and write mixed numbers.
• Convert an improper fraction to a mixed number.
• Rename fractions with a common denominator.
• Add and subtract fractions with like denominators.
• Add and subtract fractions with unlike denominators.
• Multiply fractions.
• Divide, and show a remainder as a fraction of the divisor.
• Solve word problems by modeling a fraction of a group.

Decimals

• Add, subtract, multiply, and divide decimal numbers.
• Calculate the cost per serving.
• Divide with a decimal remainder.
• Represent money with a dollar sign and decimal point.

Statistics and Probability

• Conduct a survey.
• Collect, sort, and record data.
• Find the range, mean, median, and mode of a set of data.
• Solve problems using graphs, charts, and tables.
• Make an inference, and experiment to test the inference.
• Predict the most likely or least likely outcome in a probability experiment.
• Understand theoretical and experimental probability.
• Use experimental probability to make a prediction.
• State probability as a fraction.
• Make arrangements that represent the number of possibility combinations of items from a set.
• Use a calculator to compute averages.

Graphing

• Use simple picture graphs, bar graphs, circle graphs, line graphs, tables, and charts to solve problems and record information.
• Compare information and draw conclusions using graphs.
• Collect, organize, describe, and display data using Venn diagrams.
• Graph coordinates on a coordinate plane.
• Write the coordinates of a point on a coordinate plane.