Math Secular Homeschool Curriculum Skills List | Fifth Grade

Math skills are introduced with manipulative activities that help the child see and work through the concept in a tactile manner. This is followed by an individual activity or practice worksheet (included in the lesson).

Whole Numbers and Sets

• Skip count by different increments.
• Recognize, read aloud, and write the numerals in order from zero through hundred millions.
• 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.
• Identify the value of Roman numerals.
• Identify even and odd numbers.
• Identify the number of digits in a number.
• 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 a given place value.
• Round a repeating and non-repeating decimal number.
• Write numbers in standard, expanded, and word form.
• Estimate sums and differences up to 100.
• Continue to develop the ability to understand and use ordinal numbers and words.
• Apply ordinals to daily experiences.
• Compare sets and determine if one set is equal to, greater than, or less than the other set.
• Use comparison symbols (<, =, >).
• Develop mental math skills.
• Write dictated numbers.
• Express a relationship between numbers as a ratio.
• Understand the difference between a prime and composite number.
• Write the prime factorization of a composite number.
• Find the greatest common factor of two numbers.
• Find the least common multiple.

Patterns and Operations: Algebraic Thinking

• Review addition facts 0-20.
• Review subtraction facts 0-20.
• Write addition and subtraction fact families.
• Understand that addition and subtraction are inverse operations.
• Create mathematical equations.
• Identify a missing addend.
• Use manipulatives to model and solve multiplication problems.
• Recall multiplication facts 0-12.
• Recall division facts 1-12.
• Use manipulatives to model and solve division problems.
• Divide, and show a remainder as a fraction of the divisor.
• Learn and apply the divisibility rules.
• Understand that multiplication and division are inverse operations.
• Use inverse relationships to check answers.
• Copy, extend, describe, and create simple repetitive patterns.
• Identify a missing symbol in a repeating pattern.
• Identify a missing term in a sequence.
• Use a variable to represent an unknown amount.
• Use variables in contextual situations.
• Evaluate an algebraic expression.
• Write an algebraic expression for a word phrase and a word problem.
• Use inverse relationships to solve for a variable in an equation.
• Write an equation to represent a model.
• Use digits and symbols to represent mathematical statements.
• Identify and write a function rule.
• 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 Addition Property of Equality.
• Apply the Subtraction Property of Equality.
• Apply the Identity Property of Zero.
• Use the Distributive Property to solve for a variable.
• Apply knowledge of the order of operations in math.
• Use the order of operations to simplify an expression.
• Simplify exponential numbers.

Geometry

• Identify, name, and describe polygons.
• Identify angles, vertices, faces and edges.
• Classify three-dimensional figures according to the number of faces, vertices, and edges.
• Classify a triangle as equilateral, isosceles, or scalene.
• Identify, name, describe, and build three-dimensional shapes.
• Identify the interior and the exterior of a shape.
• Draw a shape according to a given measurement and calculate the perimeter.
• Calculate the area of a regular and an irregular shape using a formula.
• Find the perimeter of a regular and an irregular shape.
• Find the perimeter and area of a composite figure.
• Calculate the volume of a rectangular prism.
• 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 and radius of a circle.
• Calculate the circumference of a circle with the given diameter.
• Draw angles of a given measurement.
• Identify angles: right, acute, obtuse.
• Use a protractor.
• 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.
• Create symmetrical designs.
• Recognize or draw a reflection over a line of symmetry.
• Make a net for polyhedra.
• Recognize and draw transformations in geometry: rotation, reflection, translation.

Measurement and Estimation

• Use a ruler to measure inches, feet, yards, and centimeters.
• Measure and draw line segments to the nearest sixteenth inch.
• Measure and draw line segments to the nearest centimeter.
• Order objects by length or height.
• Arrange multi-digit numerals from least to greatest.
• Use digital and analog clocks to tell, write, and show time to the nearest minute.
• Show times using fractional parts of an hour.
• Arrange events in the correct order.
• Compare events according to duration.
• Solve problems using a calendar.
• Write a date in word and digital form.
• Read a Fahrenheit thermometer.
• Identify units of capacity: cup, pint, quart, gallon, teaspoon, tablespoon, liters, and milliliters.
• Make direct comparisons using measurable attributes such as length, weight, and capacity.
• Understand that one item may hold more or less than another item.
• Estimate the capacity of containers.
• Measure dry and liquid ingredients.
• Calculate equivalent measurements.
• Use a unit multiplier to convert measurements.
• Identify a dozen and half dozen.
• Say, write, and compute decimal numbers.
• Recognize and round decimal numbers to the nearest thousandth.

• Make a prediction, and test to determine its accuracy.
• Use simple logic to solve a problem.
• Analyze and interpret data using logical reasoning.
• Use a graphic organizer to demonstrate a decision-making process.
• Describe how the 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.
• Write a step-by-step description of a process.
• Draw a picture to illustrate a mathematical word problem.
• Answer a riddle.

Money

• Identify pennies, nickels, dimes, quarters, and dollar bills.
• Find the value of a set of coins.
• Write the value of a set of coins as a fraction of a dollar and as a decimal number.
• Write amounts of money using a dollar sign and a decimal point.
• Compare monetary amounts using an inequality symbol.
• Select coins for a given amount.
• Pay for items and make change using coins and bills.
• Add and subtract 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.
• Solve word problems using money.
• Understand that money is accepted as final payment for goods and services.
• Identify the person on United States currency.

Fractions

• Make models that represent given fractions.
• Recognize fractional parts of a given whole.
• Write a fraction to represent part of a whole.
• Compare fractions.
• Identify equivalent fractions.
• Expand a fraction to find equivalent fractions.
• Use number lines to add fractions with like denominators.
• Reduce a fraction to lowest terms.
• Identify numerator and denominator.
• Locate rational numbers on a number line.
• Use words to write a mixed number.
• Write a mixed number to represent a picture.
• Convert an improper fraction to a mixed number.
• Rename a pair of fractions using their least common denominator.
• Add and subtract fractions with like and unlike denominators.
• Multiply and divide fractions.
• Represent fractions with a circle graph.
• Convert fractions and decimal numbers to percents.

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

• Collect, sort, and tally 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.
• State probability as a fraction.
• Make arrangements that represent the number of possibility combinations of items from a set.

Graphing

• Use simple picture graphs, bar graphs, line graphs, circle 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.
• Plot ordered pairs on a coordinate plane.
• List coordinates that connect to make a design or picture.
• Recognize a positive or negative slope on a line graph.

Calculators and Computers

• Demonstrate how a calculator works.
• Use a simple calculator to add, subtract, multiply, and divide sets.