Units of Study

Through their learning in the Number System, students work to understand numbers, fractions, decimals (that have a finite or a repeating decimal representation), and percents as different representations of rational numbers. They extend addition, subtraction, multiplication, and division to all rational numbers, maintaining the properties of operations and the relationships between addition and subtraction, and multiplication and division. The standards in red are additional standards for Pre-Algebra

• NY-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. 

• NY-7.NS.1a  Describe situations in which opposite quantities combine to make 0. 

• NY-7.NS.1b Understand that addition of rational numbers; p + q is 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. 

• NY-7.NS.1c 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. 

• NY-7.NS.1d Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

• NY-7.NS.2 Apply properties of operations as strategies to add and subtract rational numbers.

• NY-7.NS.2a 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.

• 2a. 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. 

• NY-7.NS.2b 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. 

• NY-7.NS.2c  Apply properties of operations as strategies to multiply and divide rational numbers. 

• NY-7.NS.2d Convert a fraction to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. 

• NY-7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers.

• NY-8.NS.1

• NY-8.NS.2

• NY-8.EE.1

• NY-8.EE.2

• NY-8.EE.3

• NY-8.EE.4

Ratios and Proportional Relationships

• I can determine the appropriate unit rates to use in a given situation, including those with fractions.

• I can recognize, represent, and explain proportions using tables, graphs, equations, diagrams, and verbal descriptions.

• I can solve multistep and percent problems. These include simple interest, taxes, markups, gratuities, commissions, fees, percent increase and decrease, and percent error.

NYS Standards

• NY-7.RP.1* Compute unit rates associated with ratios of fractions. 

• NY-7.RP.2 Recognize and represent proportional relationships between quantities.

• NY-7.RP.2a  Decide whether two quantities are in a proportional relationship

• NY-7.RP.2b* Identify the constant of proportionality (unit rate) in tables, graphs, equations and verbal descriptions of proportional relationships.

• NY-7.RP.2c* Represent a proportional relationship using an equation.

• NY-7.RP.2d Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

• NY-7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups, and markdowns, gratuities and commissions, fees, percent increase and decrease, and percent error.

Through their learning in the Expressions, Equations, and Inequalities domains, students extend addition, subtraction, multiplication, and division to all rational numbers, maintaining the properties of operations and the relationships between addition and subtraction, and multiplication and division. They explain and interpret the rules for adding, subtracting, multiplying, and dividing with negative numbers by applying properties of operations, and view negative numbers in terms of everyday contexts. Finally, they use the arithmetic of rational numbers as they formulate expressions and equations in one variable and use these equations to solve problems.

• NY-7.EE.1 Add, subtract, factor, and expand linear expressions with rational coefficients by applying the properties of operations. 

• NY-7.EE.2 Understand that rewriting an expression in different forms in real-world and mathematical problems can reveal and explain how the quantities are related. e.g., a + 0.05a and 1.05a are equivalent expressions meaning that “increase by 5%” is the same as “multiply by 1.05.”

• NY-7.EE.3 Solve multi-step real-world and mathematical problems

• posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate. Assess the reasonableness of answers using mental computation and estimation strategies.e.g., If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

• NY-7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Note: Solving equations that contain variables on both sides is not an expectation in grade 7.

• NY-7.EE.4a Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.

Through their learning in the Statistics and Probability domain, students build on their previous work with single data distributions to compare two data distributions and address questions about differences between populations. They begin informal work with random sampling to generate data sets and learn about the importance of representative samples for drawing inferences. They extend previous understandings of simple probabilities in grade 6 to calculate probabilities of compound events.

• NY-7.SP.1 Construct and interpret box plots, find the interquartile range and determine if a data point is an outlier.

Note: Students in grade 7 are not expected to construct box plots that include outliers in the data, but are expected to interpret box plots that may contain outliers.

• NY-7.SP.3 Informally assess the degree of visual overlap of two quantitative data distributions.

• NY-7.SP.4 Use measures of center and measures of variability for quantitative data from random samples or populations to draw informal comparative inferences about the populations.

Note: Measures of the center are mean, median, and mode. The measures of variation include the range and the interquartile range.

• NY-7.SP.8 Find probabilities of compound events using organized lists, sample space tables, tree diagrams, and simulation.

• NY-7.SP.8a Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

• NY-7.SP.8b Represent sample spaces for compound events using methods such as organized lists, sample space tables, and tree diagrams. For an event described in everyday language, identify the outcomes in the sample space which compose the event. e.g., “rolling double sixes”

• NY-7.SP.8c Design and use a simulation to generate frequencies for compound events. e.g., Use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

In this unit, students solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

• NY-7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale

drawing and reproducing a scale drawing at a different scale.

• NY-7.G.2 Draw triangles when given measures of angles and/or sides, noticing when the conditions determine a unique triangle, more

than one triangle, or no triangle.

Note: Create triangles through the use of freehand drawings, materials (scaffolds may include: pipe cleaners, Legos®, and toothpicks), rulers, protractors, and/or technology.

• NY-7.G.3 Describe the two-dimensional shapes that result from slicing three-dimensional solids parallel or perpendicular to the base.

Note: Our focus is on plane sections resulting from the slicing of right rectangular prisms and right rectangular pyramids.

• NY-7.G.4 Apply the formulas for the area and circumference of a circle to solve problems.

Note: Students in grade 7 are not expected to calculate the radius of a circle given its area.

• NY-7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. Note: Students in grade 7 are limited to solving equations that involve linear expressions on one side of the equation.