How to learn Grade 6: Mathematics

Colorado academic standards: Mathematics, Grade 6

0 of 12 concepts ready to learn · Markdown, for your AI

1. Data, Statistics, and Probability · Summarize numerical data sets in relation to their context, such as by:

1. 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. Experimental probability: Record, describe, and analyse the frequency of outcomes from probability experiments to develop an understanding of relative frequency as an estimate of probability

2. Algebra and Functions · Write, read, and evaluate expressions in which letters stand for numbers.

1. Algebraic Notation: Use and interpret algebraic notation including: ab for a × b, 3y for y + y + y, a² for a × a, a/b for a ÷ b, coefficients as fractions, and brackets for grouping; read and write algebraic expressions fluently
2. 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
3. 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)

3. Number and Quantity · Order and find absolute value of rational numbers.

1. Numbers on a number line: Understand the absolute value of a rational number as its distance from zero on the number line; interpret absolute value as magnitude in real-world contexts; distinguish absolute value comparisons from ordering statements

4. Number and Quantity · Describe a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the

1. Positive and Negative Numbers: Understand positive and negative numbers as describing quantities with opposite directions or values; use them in context such as temperature, floors in a building, and bank balances

5. Number and Quantity · Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or e

1. Real-World Mathematical Modelling: Model real-world problems involving ratio, scale, volume, unit conversion, and proportional reasoning with appropriate tools, diagrams, or equations
2. Ratio Notation: Use ratio notation to describe the relationship between two or more quantities, simplify ratios to their simplest form, and convert between ratio and fraction representations
3. Bar Models for Ratios: Represent ratio and proportion problems using bar models (rectangular strips divided into equal parts labelled with quantities) and tape diagrams (segmented strips showing part-to-part and part-to-whole relationships); use these visual models to set up and solve unequal sharing, scaling, and percentage problems — drawing the diagram first, then reading off the answer
4. Dividing Quantities by Ratio: Divide a given quantity into two parts in a given part:part or part:whole ratio, and express the division as a fraction of the whole
5. Calculating Percentages: Solve problems involving the calculation of percentages of amounts (e.g. 15% of 360) and the use of percentages for comparison