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Use Proportions to Solve Problems
7.RP.2 Recognize and represent proportional relationships between quantities.
7.RP.2.C7.RP.2.C Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.
This number sense lesson focuses on using proportions to solve problems. The lesson includes research-based strategies and strategic questions that prepare students for assessments. In this lesson, students read the problem and identify the given ratio. Then, they set up a proportion using the given ratios, if necessary. Finally, they cross-multiply and solve for the unknown value by applying an inverse operation, and then they interpret the solution. In addition to the lesson, there are eight pages of Independent Practice and review with questions modeled after current adaptive testing items.
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Solve Problems Involving Tips
(Y7) Find percentages of quantities and express one quantity as a percentage of another, with and without digital technologies. (ACMNA158)
ACMNA187(Y8) Solve problems involving the use of percentages, including percentage increases and decreases, with and without digital technologies (ACMNA187)
ACMEM011(Y11-12) Calculate a percentage of a given amount (ACMEM011)
ACMEM013(Y11-12) Apply percentage increases and decreases in situations; for example, mark-ups, discounts and GST (ACMEM013)
This number sense lesson focuses on solving problems involving tips. The lesson includes research-based strategies and strategic questions that prepare students for assessments. In this lesson, students read the problem, identifying the initial tip percent and the initial amount paid. Then, they convert the tip percentage to a decimal number and calculate the tip by multiplying the tip decimal and initial amount paid. Finally, they calculate the total amount paid by adding the initial amount and the tip, and then they interpret the total amount paid in a complete sentence. In addition to the lesson, there are eight pages of Independent Practice and review with questions modeled after current adaptive testing items.
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Solve Problems Involving Discounts, Profits, and Commissions
This number sense lesson focuses on solving problems involving discounts, profits, and commissions. The lesson includes research-based strategies and strategic questions that prepare students for assessments. In this lesson, students read the problem and identify the percent discount and original price, or percent profit and original cost, or percent commission and sale amount. Then, they calculate and interpret the discounted price, selling price, or commission. In addition to the lesson, there are eleven pages of Independent Practice and review with questions modeled after current adaptive testing items.
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Calculate the Amount of Interest Earned
This number sense lesson focuses on calculating the amount of interest earned. The lesson includes research-based strategies and strategic questions that prepare students for assessments. In this lesson, students write the known values for the interest formula by converting the rate (percent) to a decimal and the time/term (t) to years, if needed. Then, they substitute the known values in the formula and solve simple interest. Finally, they interpret the answer in a complete sentence. In addition to the lesson, there are four pages of Independent Practice and review with questions modeled after current adaptive testing items.
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Identify the Constant of Proportionality
This algebra and functions lesson focuses on solving problems involving direct variation. The lesson includes research-based strategies and strategic questions that prepare students for assessments. In this lesson, students read the question and identify which two quantities have a direct variation. Then, they set up the direct variation equation, y=kx, and solve for the constant of variation, k, by substituting the known quantities. Finally, they write and circle the direct variation equation and use it to solve for the unknown quantity. In addition to the lesson, there are eight pages of Independent Practice and review with questions modeled after current adaptive testing items.
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Solve Problems Involving Rates
This algebra and functions lesson focuses on solving problems involving rates. The lesson includes research-based strategies and strategic questions that prepare students for assessments. In this lesson, students read the problem and identify the known rate and any information about the unknown rate. Then, they set up a proportion using the known rate and the unknown rate. Finally, they solve for the unknown quantity by cross-multiplying and solving the equation, and then interpret the solution in a complete sentence. In addition to the lesson, there are four pages of Independent Practice and review with questions modeled after current adaptive testing items.
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Solve Problems Involving Markups and Discounts
This number sense lesson focuses on solving problems involving markups and discounts. The lesson includes research-based strategies and strategic questions that prepare students for assessments. In this lesson, students read the problem, identifying the original price and the percent. Then, they identify if it is a markup or discount, and convert the percent markup or discount to a decimal number. Finally, they calculate the markup or discount in dollars and then calculate the final price. In addition to the lesson, there are four pages of Independent Practice and review with questions modeled after current adaptive testing items.
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Add & Subtract on a Number Line
7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
7.NS.1.B7.NS.1.B Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.
7.NS.1.C7.NS.1.C Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.
7.NS.1.D7.NS.1.D Apply properties of operations as strategies to add and subtract rational numbers.
This number system lesson covers how to add and subtract on a number line. The lesson includes research-based strategies and strategic questions that prepare students for assessments. In this lesson, students first rewrite subtraction to add the opposite if needed. Then, they locate the first addend on the number line and move the distance of the second addend. Finally, they interpret the answer.
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Add & Subtract Rational Numbers
7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
7.NS.1.D7.NS.1.D Apply properties of operations as strategies to add and subtract rational numbers.
This number system lesson covers how to add and subtract rational numbers. The lesson includes research-based strategies and strategic questions that prepare students for assessments. In this lesson, students first rewrite subtraction to add the opposite if needed. Then, they determine which addition rule to use, apply it, and interpret the answer.
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Determine the Multiplicative Inverse of a Number
(Y6) Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers (ACMNA123)
ACMNA183(Y8) Carry out the four operations with rational numbers and integers, using efficient mental and written strategies and appropriate digital technologies (ACMNA183)
This number system lesson covers how to determine the multiplicative inverse of a number. The lesson includes research-based strategies and strategic questions that prepare students for assessments. In this lesson, students identify the given number, then determine its multiplicative inverse by switching the numerator and denominator. Finally, they interpret what it means, showing that a given number times it’s multiplicative inverse equals one.
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Compare Fractions and Decimal Numbers
This number sense lesson focuses on comparing fractions and decimal numbers. The lesson includes research-based strategies and strategic questions that prepare students for assessments. In this lesson, students change the fraction to a decimal number and line up the decimal numbers by place value. Then, they compare each digit starting from the left, noting whether the digits have the same value or if one is greater. Finally, they complete the number sentence, writing the correct comparison symbol. In addition to the lesson, there are four pages of Independent Practice and review with questions modeled after current adaptive testing items.
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Add Integers (Sign Rules)
7.NS.1.B Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.
7.NS.1.D7.NS.1.D Apply properties of operations as strategies to add and subtract rational numbers.
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Add and Subtract Fractions with Unlike Denominators
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Subtract Integers (Sign Rules)
This number sense lesson focuses on subtracting integers. The lesson includes research-based strategies and strategic questions that prepare students for assessments. In this lesson, students read the problem and change the subtraction problem to add the opposite. Then, they use the given addition integer rules to solve, identifying whether the answer has the same sign or different sign. In addition to the lesson, there are four pages of Independent Practice and review with questions modeled after current adaptive testing items.
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Convert Rational Numbers to Decimals
This number sense lesson focuses on converting rational numbers (as fractions) to decimals. The lesson includes research-based strategies and strategic questions that prepare students for assessments. In this lesson, students identify the numerator and denominator of the fraction. Then, they convert the fraction to a decimal by using long division to divide the numerator by the denominator, inserting placeholder zeroes until the division is complete, and aligning place values to correctly place the decimal point. Finally, they interpret the answer. In addition to the lesson, there are four pages of Independent Practice and review with questions modeled after current adaptive testing items.
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Convert Fractions to Percents
This number sense lesson focuses on converting fractions to percents. The lesson includes research-based strategies and strategic questions that prepare students for assessments. In this lesson, students set up an equation using the percent proportion and the given fraction. Then, they cross multiply and solve the proportion. Finally, they state their answer as a percent by using the provided sentence. In addition to the lesson, there are four pages of Independent Practice and review with questions modeled after current adaptive testing items.
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Convert Percents to Decimals
This number sense lesson focuses on converting percents to decimals. The lesson includes research-based strategies and strategic questions that prepare students for assessments. In this lesson, students rewrite the percent as a decimal by moving the decimal point two places to the left and removing the percent symbol. Finally, they interpret their answer. In addition to the lesson, there are four pages of Independent Practice and review with questions modeled after current adaptive testing items.
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Multiply & Divide Integers
7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
7.NS.2.A7.NS.2.A Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.
7.NS.2.B7.NS.2.B Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts.
7.NS.2.C7.NS.2.C Apply properties of operations as strategies to multiply and divide rational numbers.