How to learn Grade 5: Mathematics

Department of Defense Education Activity standards: Mathematics, Grade 5

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1. Mathematics

1. Classifying shapes by properties: Compare and classify geometric shapes based on their properties and sizes; understand that attributes belonging to a category also belong to all subcategories; classify two-dimensional figures in a hierarchy based on properties
2. Numbers on a number line: Understand a coordinate system defined by two perpendicular number lines (axes) with an origin at (0,0); know that an ordered pair (x, y) specifies a unique point where the first number gives horizontal distance and the second gives vertical distance from the origin
3. Plotting points in the first quadrant: Plot and read ordered pairs in the first quadrant of the coordinate plane; represent real-world and mathematical problems by graphing points and interpreting coordinate values in context
4. Volume as additive: Recognise volume as additive; find volumes of composite solid figures made of two or more non-overlapping right rectangular prisms
5. Measuring length (age 10+): Recognise volume as an attribute of solid figures; understand that a unit cube (side length 1 unit) has 'one cubic unit' of volume and can be used to measure volume; a solid packed with n unit cubes has volume n cubic units
6. Counting Unit Cubes: Measure volumes by counting unit cubes using cubic cm, cubic in, cubic ft, and other units
7. Adding Fractions (Unlike Denominators): Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions to produce a common denominator
8. Understanding fractions: Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8); use operations on fractions to solve problems involving data in line plots (e.g. redistribute total equally)
9. Measurement Conversions: Solve problems involving the calculation and conversion of units of measure, using decimal notation and multi-step reasoning in real-world contexts
10. Fractions of a whole (age 10+): Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b); solve word problems involving division of whole numbers leading to fractional or mixed-number answers
11. Multiplying fractions (age 10+): Multiply a fraction or whole number by a fraction, including proper fractions by proper fractions; interpret (a/b) × q as a parts of q partitioned into b equal parts; write answers in simplest form
12. Dividing fractions (unit fractions): Interpret and compute division of a unit fraction by a non-zero whole number (e.g. 1/3 ÷ 4 = 1/12); use visual models and the relationship between multiplication and division to explain the result
13. Real-world fraction multiplication: Solve real-world problems involving multiplication of fractions and mixed numbers, using visual fraction models or equations
14. Multiplication as scaling: Interpret multiplication as scaling (resizing): compare the size of a product to a factor based on the size of the other factor without computing; explain the effect of multiplying by fractions greater than, equal to, or less than 1
15. Fraction Word Problems: Solve word problems involving addition and subtraction of fractions with unlike denominators, using visual models and benchmark fractions to estimate and assess reasonableness
16. Reading and writing numbers (age 10+): Read, write, and compare decimals to thousandths using base-ten numerals, number names, and expanded form; compare using >, =, < based on place-value meaning
17. Fluent addition and subtraction (age 9+): Fluently add and subtract whole numbers with more than four digits using the standard columnar algorithm
18. Addition and subtraction strategies (age 10+): Add and subtract decimals to hundredths using strategies based on place value, properties of operations, and the relationship between addition and subtraction; relate strategies to written methods and explain reasoning
19. Dividing by Fractions: Interpret and compute division of a whole number by a unit fraction (e.g. 4 ÷ 1/5 = 20); use visual models and the relationship between multiplication and division to explain why the quotient is larger than the dividend
20. Decimal place value: Round decimals to any place using place-value understanding; round any whole number to a required degree of accuracy
21. Place Value × 10 and ÷ 10: Recognise that in a multi-digit number, a digit in one place represents 10 times as much as in the place to its right and 1/10 of what it represents in the place to its left
22. Patterns with Powers of Ten: Explain patterns in zeros when multiplying by powers of 10 and in decimal-point placement when multiplying/dividing by a power of 10; use whole-number exponents to denote powers of 10 (e.g. 10³ = 1000)
23. Number Pattern Relationships: Generate two numerical patterns using two given rules; identify relationships between corresponding terms; form ordered pairs and graph them on a coordinate plane
24. Brackets in Expressions: Use parentheses, brackets, or braces in numerical expressions and evaluate expressions containing these grouping symbols
25. Writing Number Sentences: Write simple numerical expressions that record calculations with numbers, and interpret numerical expressions without evaluating them (e.g. recognise that 3 × (18932 + 921) is three times as large as 18932 + 921)