How to learn Grade 5: Mathematics

Minnesota academic standards: Mathematics, Grade 5

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1. Data Analysis · Display and interpret data; determine mean, median and range.

Statistical Analysis Vocabulary: Read, write, and use the vocabulary of statistical analysis — mean, median, mode, range, frequency, data, sample, average, chart, table, graph, pie chart, scatter graph, correlation — with understanding of what each term describes
Comparing measurements: Describe, interpret, and compare distributions of a single variable using appropriate measures of central tendency (mean, median, mode) and spread (range), including the effect of outliers

2. Geometry & Measurement · Determine the area of triangles and quadrilaterals; determine the surface area and volume of rectangular prisms in various contexts.

Area of Triangles & Parallelograms: Calculate the area of parallelograms and triangles using formulae (A = b × h for parallelograms, A = ½ × b × h for triangles)
Counting Unit Cubes: Measure volumes by counting unit cubes using cubic cm, cubic in, cubic ft, and other units
Estimating answers (age 10+): Find the volume of right rectangular prisms by packing with unit cubes and show it equals l × w × h (or base area × height); apply V = l × w × h and V = B × h to solve real-world problems; calculate, estimate, and compare volumes of cubes and cuboids in standard units (cm³, m³)
Angles in triangles (age 11+): Derive and apply formulae for the area of triangles, parallelograms, and trapezia, and for the volume of cuboids and other prisms (including cylinders), connecting each formula to its geometric reasoning

3. Geometry & Measurement · Describe, classify, and draw representations of three-dimensional figures.

Nets of 3-D Shapes: Identify, draw, and interpret nets of common 3-D shapes — cubes, cuboids, triangular prisms, and square-based pyramids — by predicting which 3-D shape a given flat arrangement of faces will fold into, checking whether a net will close completely, and sketching a net from a description or 3-D model; understand the relationship between the number of faces and the structure of the net
3-D shapes (age 10+): Recognise, describe, and build simple 3-D shapes, including making nets
3-D shapes (age 11+): Use the properties of faces, surfaces, edges, and vertices of 3-D shapes (cubes, cuboids, prisms, cylinders, pyramids, cones, and spheres) to solve problems, including visualising cross-sections

4. Algebra · Understand and interpret equations and inequalities involving variables and whole numbers, and use them to represent and solve real-world and mathematical problems.

Expressions & Equations Vocabulary: Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms, and factors; distinguish between an expression (no equals sign), an equation (equals sign), and an inequality (inequality sign)
Algebraic Transformations: Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs; move between word problems, algebraic representations, tables, and graphical representations

5. Algebra · Use properties of arithmetic to generate equivalent numerical expressions and evaluate expressions involving whole numbers.

Substituting into Formulae: Substitute numerical values into formulae and expressions including scientific formulae; evaluate expressions by replacing variables with given values and computing the result using correct order of operations

6. Number & Operation · Add and subtract fractions, mixed numbers and decimals to solve real-world and mathematical problems.

Mixed & Improper Fractions: Use the four operations with formal written methods applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative
Fraction Addition Concepts: Understand addition and subtraction of fractions as joining and separating parts; decompose a fraction into a sum of fractions with the same denominator in more than one way
Adding and subtracting mixed numbers: Add and subtract mixed numbers with like denominators, including by converting to improper fractions or using properties of operations
Real-world fraction multiplication: Solve real-world problems involving multiplication of fractions and mixed numbers, using visual fraction models or equations

7. Number & Operation · Read, write, represent and compare fractions and decimals; recognize and write equivalent fractions; convert between fractions and decimals; use fractions and decimals in real-wor

Decimal & Percent Notation: Read, write, and use decimal and percentage notation correctly — decimal, decimal point, tenths, hundredths, thousandths, percentage, per cent, % symbol, convert, terminating decimal — and understand the relationships between fractions, decimals, and percentages as three ways of expressing the same value
Decimals for Tenths & Hundredths: Use decimal notation for fractions with denominators 10 or 100; read and write decimal numbers as fractions (e.g. 0.62 = 62/100, 0.71 = 71/100)
Fractions on a number line: Understand and use place value for decimals, measures, and integers of any size; extend the number system to include all positive and negative integers, decimals, and fractions on a single number line
Fractions on a number line (age 11+): Order positive and negative integers, decimals, and fractions on a number line; use the symbols =, ≠, <, >, ≤, ≥ to compare values including negative numbers and mixed representations
Percentages as Fractions: Define percentage as 'number of parts per hundred'; interpret percentages and percentage changes as a fraction or a decimal; express one quantity as a percentage of another; compare quantities using percentages; work with percentages greater than 100%
Decimals and fractions (age 10+): Associate a fraction with division and calculate decimal fraction equivalents for simple fractions (e.g. 3/8 = 0.375); recall and use equivalences between simple fractions, decimals, and percentages in different contexts

8. Number & Operation · Divide multi-digit numbers; solve real-world and mathematical problems using arithmetic.

Division with remainders (age 10+): Divide numbers up to 4 digits by a two-digit divisor using formal written long division, interpreting remainders as whole numbers, fractions, or by rounding as appropriate
Multi-step problems: choosing operations: Solve problems involving addition, subtraction, multiplication, and division, deciding which operations and methods to use and why; solve multi-step problems in contexts
Dividing by two-digit numbers: Divide numbers up to 4 digits by a two-digit number using formal written short division where appropriate, interpreting remainders according to context
Division with Decimals: Use written division methods in cases where the answer has up to two decimal places; divide decimals to hundredths by whole numbers