Math Chapter 1: Use Place Value
Standards
5.1.1a Convert between whole numbers in words and standard form for numbers up to millions.
5.1.1b Covert between numbers in words and standard form for decimals to thousandths.
5.1.1c Write decimals to thousandths in expanded form.
Description: 347.39 = (3 x 100) + (4 x 10) + (7 x 1) + (3 x 1/10) + (9 x 1/100)5.1.3a Compare whole numbers using the symbols for less than (<), greater than (>) and equal (=).
5.1.3b Compare decimals to the hundredths using the symbols for less than (<), greater than (>) and equal (=).
5.1.3c Order numbers with decimals to two decimal places.
5.1.3d Explain that the place value to the right is 10 times greater than a given digit and the place value to the left is 1/10 as great as that digit.
5.1.1a Convert between whole numbers in words and standard form for numbers up to millions.
5.1.1b Covert between numbers in words and standard form for decimals to thousandths.
5.1.1c Write decimals to thousandths in expanded form.
Description: 347.39 = (3 x 100) + (4 x 10) + (7 x 1) + (3 x 1/10) + (9 x 1/100)5.1.3a Compare whole numbers using the symbols for less than (<), greater than (>) and equal (=).
5.1.3b Compare decimals to the hundredths using the symbols for less than (<), greater than (>) and equal (=).
5.1.3c Order numbers with decimals to two decimal places.
5.1.3d Explain that the place value to the right is 10 times greater than a given digit and the place value to the left is 1/10 as great as that digit.
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Study GuideCh. 1 & 3 Study Guide (Place Value + Multiplication)
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Math Unit 2: Add & Subtract Whole Numbers & Decimals
Standards
5.1.2a Round whole numbers to any place value.
5.1.2b Round decimals to any place value.
5.2.5b Estimate to determine whether sums of decimal numbers are reasonable.
5.2.6a Estimate to determine whether answers are reasonable in addition, subtraction, multiplication and division problems.
5.2.6b Explain orally and in writing whether answers are reasonable in addition, subtraction, multiplication and division problems.
5.2.5a Add and subtract decimals.
5.2.7a Use mental arithmetic to add or subtract simple decimals.
5.5.7a Add with money in decimal notation.
5.5.7b Subtract with money in decimal notation.
5.1.2a Round whole numbers to any place value.
5.1.2b Round decimals to any place value.
5.2.5b Estimate to determine whether sums of decimal numbers are reasonable.
5.2.6a Estimate to determine whether answers are reasonable in addition, subtraction, multiplication and division problems.
5.2.6b Explain orally and in writing whether answers are reasonable in addition, subtraction, multiplication and division problems.
5.2.5a Add and subtract decimals.
5.2.7a Use mental arithmetic to add or subtract simple decimals.
5.5.7a Add with money in decimal notation.
5.5.7b Subtract with money in decimal notation.
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Math Unit 3: Multiply Whole Numbers
Standards
5.2.1a Multiply any number by a multiple of 10.
5.2.1c Multiply any number by a multiple of 100.
5.3.3c Solve problems using the distributive property.
Description: Note: This would be a great time to name and review the commutative and associative properties of addition and multiplication.
5.2.6a Estimate to determine whether answers are reasonable in addition, subtraction, multiplication and division problems.
5.2.6b Explain orally and in writing whether answers are reasonable in addition, subtraction, multiplication and division problems.
5.2.1e Multiply any whole number by any whole number.
5.2.1b Multiply any number by a two-digit number.
5.2.1d Multiply any number by a triple digit number.
5.2.1a Multiply any number by a multiple of 10.
5.2.1c Multiply any number by a multiple of 100.
5.3.3c Solve problems using the distributive property.
Description: Note: This would be a great time to name and review the commutative and associative properties of addition and multiplication.
5.2.6a Estimate to determine whether answers are reasonable in addition, subtraction, multiplication and division problems.
5.2.6b Explain orally and in writing whether answers are reasonable in addition, subtraction, multiplication and division problems.
5.2.1e Multiply any whole number by any whole number.
5.2.1b Multiply any number by a two-digit number.
5.2.1d Multiply any number by a triple digit number.
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Math Unit 4: Divide Whole Numbers
Standards
5.2.1f Divide any whole number by a multiple of 10.
5.2.1j Divide any whole number by a smaller whole number.
5.2.1g Divide any whole number by a two-digit divisor.
5.2.1h Divide any whole number by a three-digit divisor.
5.2.1i Divide any whole number with zero in the quotient.
5.2.1f Divide any whole number by a multiple of 10.
5.2.1j Divide any whole number by a smaller whole number.
5.2.1g Divide any whole number by a two-digit divisor.
5.2.1h Divide any whole number by a three-digit divisor.
5.2.1i Divide any whole number with zero in the quotient.
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Math Unit 5: Use Algebraic Expressions
Standards
5.3.1a Use a variable to represent an unknown number.
5.3.2a Evaluate algebraic expressions with one or two variables through substitution.
5.3.2b Write simple algebraic expressions with one or two variables.
5.3.3a Solve equations involving parentheses, brackets, or braces.
5.3.3b Write equations using parentheses, brackets, or braces.
5.3.1a Use a variable to represent an unknown number.
5.3.2a Evaluate algebraic expressions with one or two variables through substitution.
5.3.2b Write simple algebraic expressions with one or two variables.
5.3.3a Solve equations involving parentheses, brackets, or braces.
5.3.3b Write equations using parentheses, brackets, or braces.
Math Unit 6: Equations & Function Tables
Standards
5.3.2a Evaluate algebraic expressions with one or two variables through substitution.
5.3.2b Write simple algebraic expressions with one or two variables.
5.3.4a Identify the x and y axes on a coordinate plane.
5.3.4b Explain that the x-axis is a horizontal number line and the y-axis is a vertical number line.
5.3.4c Plot ordered pairs of positive numbers on a coordinate plane.
5.3.5a Plot ordered pairs on graph paper and connect them with a line.
5.3.5b Create a table of values for x and y that satisfy a given linear equation.
5.3.5c Determine ordered pairs for a linear equation.
5.3.6a Find the distance between two points on a horizontal line on a coordinate plane.
5.3.6b Find the distance between two points on a vertical line on a coordinate plane.
5.3.6c Find the distance between two points on a vertical or horizontal line on a coordinate plane given only the ordered pair.
5.3.7a Answer questions using information from a graph or diagram.
5.3.7b Solve problems using information from equations.
5.3.2a Evaluate algebraic expressions with one or two variables through substitution.
5.3.2b Write simple algebraic expressions with one or two variables.
5.3.4a Identify the x and y axes on a coordinate plane.
5.3.4b Explain that the x-axis is a horizontal number line and the y-axis is a vertical number line.
5.3.4c Plot ordered pairs of positive numbers on a coordinate plane.
5.3.5a Plot ordered pairs on graph paper and connect them with a line.
5.3.5b Create a table of values for x and y that satisfy a given linear equation.
5.3.5c Determine ordered pairs for a linear equation.
5.3.6a Find the distance between two points on a horizontal line on a coordinate plane.
5.3.6b Find the distance between two points on a vertical line on a coordinate plane.
5.3.6c Find the distance between two points on a vertical or horizontal line on a coordinate plane given only the ordered pair.
5.3.7a Answer questions using information from a graph or diagram.
5.3.7b Solve problems using information from equations.
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Math Unit 7: Display & Interpret Data
Standards
5.6.2a Define the mean of a data set.
5.6.2b Define the median of a data set.
5.6.2c Define the mode of a data set.
5.6.2e Find the mean of a data set.
5.6.2f Find the median of a data set.
5.6.2g Find the mode of a data set.
5.6.2d Define the range of a data set.
5.6.2h Find the range of a data set.
5.6.1b Explain the purpose of each type of data display.
Description: line plot: for data distribution
circle graph: shows relative parts of a whole
line graph: shows change
bar graph: shows comparison
picture graph: shows comparison
frequency table: organizes data
5.6.1a Create a line graph to organize data.
5.6.1c Choose and explain which types of displays are appropriate for various sets of data.
5.6.1d Complete missing information in tables, charts, or graphs.
5.6.2a Define the mean of a data set.
5.6.2b Define the median of a data set.
5.6.2c Define the mode of a data set.
5.6.2e Find the mean of a data set.
5.6.2f Find the median of a data set.
5.6.2g Find the mode of a data set.
5.6.2d Define the range of a data set.
5.6.2h Find the range of a data set.
5.6.1b Explain the purpose of each type of data display.
Description: line plot: for data distribution
circle graph: shows relative parts of a whole
line graph: shows change
bar graph: shows comparison
picture graph: shows comparison
frequency table: organizes data
5.6.1a Create a line graph to organize data.
5.6.1c Choose and explain which types of displays are appropriate for various sets of data.
5.6.1d Complete missing information in tables, charts, or graphs.
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Math Unit 8: Developing Fraction Concepts
Standards
5.1.5a Explain different interpretations of fractions: parts of a whole, set, division of who numbers by whole numbers (orally, written, and/or w/ pictures)
What fraction of a pizza will each person get when 3 pizzas are divided equally among 5 people? (3 ÷ 5 = 3/5 )
5.1.7 a-d plot fractions, mixed numbers, and decimals on a number line
5.1.5a Explain different interpretations of fractions: parts of a whole, set, division of who numbers by whole numbers (orally, written, and/or w/ pictures)
What fraction of a pizza will each person get when 3 pizzas are divided equally among 5 people? (3 ÷ 5 = 3/5 )
5.1.7 a-d plot fractions, mixed numbers, and decimals on a number line
Math Unit 9: Use Factors & Multiples
Standards
5.1.6a List factors of whole numbers.
5.1.6b Explain that a prime number is a number that can be evenly divided only by 1 and itself (e.g., 2, 3, 5, 7, 11).
5.1.6c Explain that a composite number is a number with more than two factors (e.g., 4, 6, 8, 9, 10).
5.1.6d Identify prime and composite numbers by listing factors.
5.2.2c Find equivalent fractions through multiplication or division of numerators and denominators.
5.2.2a List multiples of whole numbers up to 10.
5.2.2b Identify common multiples of whole numbers up to 10.
5.1.6a List factors of whole numbers.
5.1.6b Explain that a prime number is a number that can be evenly divided only by 1 and itself (e.g., 2, 3, 5, 7, 11).
5.1.6c Explain that a composite number is a number with more than two factors (e.g., 4, 6, 8, 9, 10).
5.1.6d Identify prime and composite numbers by listing factors.
5.2.2c Find equivalent fractions through multiplication or division of numerators and denominators.
5.2.2a List multiples of whole numbers up to 10.
5.2.2b Identify common multiples of whole numbers up to 10.
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Math Unit 10: Add & Subtract Fractions
Standards
5.2.2d Add and subtract fractions with different denominators.
Description: Example: 1/2 + 2/5 = 5/10 + 4/10 = 9/10
5.2.2e Add mixed numbers with different denominators (with and without regrouping).
Description: Example: 3 4/5 + 2 2/3 = 3 12/15 + 2 10/15 = 5 22/15 = 6 7/15
5.2.2f Subtract mixed numbers with different denominators (with and without regrouping).
Description: Without: 3 4/5 - 2 2/3 = 3 12/15 - 2 10/15 = 1 2/15
With: 3 1/2 - 2 3/4 = 3 2/4 - 2 3/4 = 2 6/4 - 2 3/4 = 3/4
5.2.3a Represent multiplication of fractions with models.
5.2.3b Represent division of fractions with models.
5.2.4a Multiply fractions to solve problems.
5.2.4b Divide fractions to solve problems.
5.2.2d Add and subtract fractions with different denominators.
Description: Example: 1/2 + 2/5 = 5/10 + 4/10 = 9/10
5.2.2e Add mixed numbers with different denominators (with and without regrouping).
Description: Example: 3 4/5 + 2 2/3 = 3 12/15 + 2 10/15 = 5 22/15 = 6 7/15
5.2.2f Subtract mixed numbers with different denominators (with and without regrouping).
Description: Without: 3 4/5 - 2 2/3 = 3 12/15 - 2 10/15 = 1 2/15
With: 3 1/2 - 2 3/4 = 3 2/4 - 2 3/4 = 2 6/4 - 2 3/4 = 3/4
5.2.3a Represent multiplication of fractions with models.
5.2.3b Represent division of fractions with models.
5.2.4a Multiply fractions to solve problems.
5.2.4b Divide fractions to solve problems.
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Math Unit 11: Customary Measurement
Standards
5.5.5b Use smaller and larger Standard units for measuring weight.
Description: ounce and pound
5.5.5d Convert ounces to pounds and pounds to ounces
5.5.5b Use smaller and larger Standard units for measuring weight.
Description: ounce and pound
5.5.5d Convert ounces to pounds and pounds to ounces
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Math Unit 12: Metric Measurement
Standards
5.5.5a Use smaller and larger Metric units for measuring weight.
Description: gram and kilogram
5.5.5c Convert grams to kilograms and kilograms to grams.
5.5.6a Compare temperatures in Celsius and Fahrenheit.
5.5.6b Explain that the freezing point of water is 0°C and 32°F.
5.5.6c Explain that the boiling point of water is 100°C and 212°F.
5.5.5a Use smaller and larger Metric units for measuring weight.
Description: gram and kilogram
5.5.5c Convert grams to kilograms and kilograms to grams.
5.5.6a Compare temperatures in Celsius and Fahrenheit.
5.5.6b Explain that the freezing point of water is 0°C and 32°F.
5.5.6c Explain that the boiling point of water is 100°C and 212°F.
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Math Unit 13: Geometric Figures
Standards
5.4.1c Draw perpendicular and parallel lines.
5.4.1d Construct rectangles and triangles given specific measurements.
5.4.1e/5.4.5a Identify radius and diameter of circles.
5.4.1f/5.4.5b Draw radius and diameter of circles.
5.4.1g Measure radius and diameter of circles.
5.4.1h Construct circles given specific measurements using a compass.
5.4.1b Draw angles using a protractor.
5.4.1a Measure degrees using a protractor.
Description: Concept of the unit of degrees for measurement of angles is based on the 360º in a circle.
5.4.2a Identify triangles by their sides.
Description: equilateral, isoceles, scalene
5.4.2b Describe triangles by their sides.
5.4.2c Draw triangles by their sides.
5.4.2d Classify triangles by their sides.
5.4.2e Identify triangles by their angles.
Description: right, acute, obtuse and equiangluar
5.4.2f Describe triangles by their angles.
5.4.2g Draw triangles by their angles.
5.4.2h Classify triangles by their angles.
5.4.4a Identify polygons.
5.4.4b Describe polygons.
5.4.4c Draw polygons.
5.4.4d Classify polygons.
5.4.6a Identify shapes that have reflectional symmetry.
5.4.6b Identify shapes that have rotational symmetry.
5.4.7a Match 90°, 180°, 270°, and 360° with quarter, half, three-quarters, and full turns, respectively.
5.4.3a Identify congruent triangles by their sides and angles.
5.4.1c Draw perpendicular and parallel lines.
5.4.1d Construct rectangles and triangles given specific measurements.
5.4.1e/5.4.5a Identify radius and diameter of circles.
5.4.1f/5.4.5b Draw radius and diameter of circles.
5.4.1g Measure radius and diameter of circles.
5.4.1h Construct circles given specific measurements using a compass.
5.4.1b Draw angles using a protractor.
5.4.1a Measure degrees using a protractor.
Description: Concept of the unit of degrees for measurement of angles is based on the 360º in a circle.
5.4.2a Identify triangles by their sides.
Description: equilateral, isoceles, scalene
5.4.2b Describe triangles by their sides.
5.4.2c Draw triangles by their sides.
5.4.2d Classify triangles by their sides.
5.4.2e Identify triangles by their angles.
Description: right, acute, obtuse and equiangluar
5.4.2f Describe triangles by their angles.
5.4.2g Draw triangles by their angles.
5.4.2h Classify triangles by their angles.
5.4.4a Identify polygons.
5.4.4b Describe polygons.
5.4.4c Draw polygons.
5.4.4d Classify polygons.
5.4.6a Identify shapes that have reflectional symmetry.
5.4.6b Identify shapes that have rotational symmetry.
5.4.7a Match 90°, 180°, 270°, and 360° with quarter, half, three-quarters, and full turns, respectively.
5.4.3a Identify congruent triangles by their sides and angles.
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Math Unit 14: Perimeter, Area, & Volume
Standards
5.5.2a Solve problems involving perimeters of rectangles, triangles, parallelograms, and trapezoids, using appropriate units.
5.NF.4b Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
Description: This aligns partially with 4.5.4 and 5.5.2. The CCSS emphasizes fractional side lengths.
5.5.2b Solve problems involving areas of rectangles, triangles, parallelograms, and trapezoids, using appropriate units.
5.5.3a Find the area of complex shapes by dividing them into basic shapes and using formulas for the areas of rectangles and triangles.
5.5.4b Find the volume of rectangular solids using appropriate units.
5.5.4a Find the surface area of rectangular solids using appropriate units.
5.5.2a Solve problems involving perimeters of rectangles, triangles, parallelograms, and trapezoids, using appropriate units.
5.NF.4b Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
Description: This aligns partially with 4.5.4 and 5.5.2. The CCSS emphasizes fractional side lengths.
5.5.2b Solve problems involving areas of rectangles, triangles, parallelograms, and trapezoids, using appropriate units.
5.5.3a Find the area of complex shapes by dividing them into basic shapes and using formulas for the areas of rectangles and triangles.
5.5.4b Find the volume of rectangular solids using appropriate units.
5.5.4a Find the surface area of rectangular solids using appropriate units.
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Math Unit 15: Probability
Standards
5.6.3a Explain that events that are not going to happen have a probability of 0.
5.6.3b Explain that events that are certain to happen have a probability of 1.
5.6.3c Explain that probabilities that are more likely to occur have a higher numerical probability.
5.6.4a Give the experimental probability of a situation verbally and numerically.
5.6.3a Explain that events that are not going to happen have a probability of 0.
5.6.3b Explain that events that are certain to happen have a probability of 1.
5.6.3c Explain that probabilities that are more likely to occur have a higher numerical probability.
5.6.4a Give the experimental probability of a situation verbally and numerically.
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