All Lessons

(B) Apply qualitative and quantitative reasoning to solve prediction and comparison of real-world problems involving ratios and rates

(A) Represent mathematical and real-world problems involving ratios and rates using scale factors, tables, graphs, and proportions

(Y8) Solve a range of problems involving rates and ratios, with and without digital technologies (ACMNA188)

6.RP.3 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 equations.

6.RP.3.A Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

(B) Solve real-world problems to find the whole given a part and the percent, to find the part given the whole and the percent, and to find the percent given the part and the whole, including the use of concrete and pictorial models

(Y6) Investigate and calculate percentage discounts of 10%, 25% and 50% on sale items, with and without digital technologies (ACMNA132)

6.RP.3 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 equations.

6.RP.3.A Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

6.RP.3.C Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

(G) Generate equivalent forms of fractions, decimals, and percents using real-world problems, including problems that involve money

(Y6) Make connections between equivalent fractions, decimals and percentages (ACMNA131)

6.RP.3.C Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

(D) Give examples of rates as the comparison by division of two quantities having different attributes, including rates as quotients

(Y8) Solve a range of problems involving rates and ratios, with and without digital technologies (ACMNA188)

6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes."

6.RP.3 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 equations.

6.RP.3.A Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

6.RP.3.B Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?

(B) Solve real-world problems to find the whole given a part and the percent, to find the part given the whole and the percent, and to find the percent given the part and the whole, including the use of concrete and pictorial models

(Y8) Solve problems involving the use of percentages, including percentage increases and decreases, with and without digital technologies (ACMNA187)

6.RP.3.C Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

(A) Add and subtract whole numbers and decimals to the hundredths place using the standard algorithm

(Y6) Add and subtract decimals, with and without digital technologies, and use estimation and rounding to check the reasonableness of answers (ACMNA128)

6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

(C) Give examples of ratios as multiplicative comparisons of two quantities describing the same attribute

6.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).

(A) Classify whole numbers, integers, and rational numbers using a visual representation such as a Venn diagram to describe relationships between sets of numbers

(Y6) Investigate everyday situations that use integers. Locate and represent these numbers on a number line (ACMNA124)

6.NS.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

(B) Identify a number, its opposite, and its absolute value

(Y6) Investigate everyday situations that use integers. Locate and represent these numbers on a number line (ACMNA124)

6.NS.6.A Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite.

(11) Measurement and data. The student applies mathematical process standards to use coordinate geometry to identify locations on a plane. The student is expected to graph points in all four quadrants using ordered pairs of rational numbers.

(Y6) Introduce the Cartesian coordinate system using all four quadrants (ACMMG143)

6.NS.6.C Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

(C) Locate, compare, and order integers and rational numbers using a number line

(Y7) Compare, order, add and subtract integers (ACMNA280)

6.NS.6 Understand 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 plane with negative number coordinates.

(C) Locate, compare, and order integers and rational numbers using a number line

(D) Order a set of rational numbers arising from mathematical and real-world contexts

(Y7) Compare fractions using equivalence. Locate and represent positive and negative fractions and mixed numbers on a number line (ACMNA152)

6.NS.6.C Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

(C) Give examples of ratios as multiplicative comparisons of two quantities describing the same attribute

(Y8) Factorise algebraic expressions by identifying numerical factors (ACMNA191)

6.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).

(C) Give examples of ratios as multiplicative comparisons of two quantities describing the same attribute

(Y5) Identify and describe factors and multiples of whole numbers and use them to solve problems (ACMNA098)

6.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).

(11) Measurement and data. The student applies mathematical process standards to use coordinate geometry to identify locations on a plane. The student is expected to graph points in all four quadrants using ordered pairs of rational numbers.

(Y6) Introduce the Cartesian coordinate system using all four quadrants (ACMMG143)

6.NS.6.C Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

(A) Recognize that dividing by a rational number and multiplying by its reciprocal result in equivalent values

(B) Determine, with and without computation, whether a quantity is increased or decreased when multiplied by a fraction, including values greater than or less than one

(E) Multiply and divide positive rational numbers fluently.

(Y7) Multiply and divide fractions and decimals using efficient written strategies and digital technologies (ACMNA154)

6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

(D) Determine the distance between two points on a coordinate plane using the Pythagorean Theorem.

(Y9) Find the distance between two points located on the Cartesian plane using a range of strategies, including graphing software (ACMNA214)

6.NS.8 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

(C) Solve with proficiency for quotients of up to a four-digit dividend by a two-digit divisor using strategies and the standard algorithm

(Y5) Solve problems involving division by a one digit number, including those that result in a remainder (ACMNA101)

6.NS.2 Fluently divide multi-digit numbers using the standard algorithm.

(E) Multiply and divide positive rational numbers fluently.

(Y7) Multiply and divide fractions and decimals using efficient written strategies and digital technologies (ACMNA154)

6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

(F) Analyze mathematical relationships to connect and communicate mathematical ideas

(Y5) Identify and describe factors and multiples of whole numbers and use them to solve problems (ACMNA098)

6.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).