Category: Grade 7 Math

Geometry

Unit description: Students will solve real-life and mathematical problems involving angle measures, area, circumference, surface area and volume.

Essential Outcomes of the Unit

Geometry- Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

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

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.

Other Standards Addressed in the Unit

Geometry- Draw, construct, and describe geometrical figures and describe the relationships between them.

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.

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.

7.G.6 Solve real-world and mathematical problems involving area of two-dimensional objects

composed of triangles and trapezoids. Solve surface area problems involving right prisms and right pyramids composed of triangles and trapezoids. Find the volume of right triangular prisms, and solve volume problems involving three dimensional objects composed of right rectangular prisms.

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

Essential Questions and Big Ideas

How do I apply my knowledge of angles to find missing measurements?

• Supplementary angles are angles that make a straight angle or 180 degrees. 
• Complementary angles are angles that make a right angle or 90 degrees.  
• Vertical angles are opposite each other when two lines intersect and they are equal.  
• Adjacent angles share a vertex.  
• Triangles have three angles that add up to 180 degrees.  

What makes a circle a circle? What does it mean to talk about the size of a circle?

• The set of points in a plane that are the same distance from another point define a circle. 
• The radius, diameter, circumference, and area of a circle are related; you can use them to talk about the size of a circle.

What are scale drawings and how are they useful? 

• Scale drawings are drawn proportional to real world measurements.  
• A scale drawing can be created to represent smaller versions of projects.  

How do I draw, construct, and describe geometrical figures and describe the relationships between them?

• The area of a shape can be found by decomposing it into known figures, such as triangles and rectangles. 
• Areas and volumes of triangular shapes can be related to rectangular shapes. 

Download the complete Grade 7 Math Unit 5 framework to customize for your own planning.

Unit description: In this unit the students will learn to gather and analyze data to make informed decisions, interpret variability  and predict future outcomes based on data analysis.

Essential Outcomes of the Unit

Statistics and Probability

Investigate chance processes and develop, use, and evaluate probability models.

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

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.

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.

7.SP.8c Design and use a simulation to generate frequencies for compound events. 

Essential Questions and Big Ideas

How do you measure the probability of an event?

• You can use words such as unlikely and certain, or a number between 0 and 1 to represent the probability that an event will occur.

How do you measure the probability of more than one event?

• A compound event is an event associated with a multi-step action. You can find the number of outcomes of a multi-step process by finding the product of the number of possible outcomes of each step of the process.

Can you use probability to predict future events?

• You can perform trials and collect data to find experimental probability. You can reason about all of the possible outcomes of an event and find theoretical probability.

 

Download the complete Grade 7 Math Unit 4 framework to customize for your own planning.

Ratios and Proportional Relationships

Unit description: In this unit, students will learn to extend knowledge of proportional relationships and ratios related to scale drawings and other real-world situations. They will represent a relationship between two quantities by identifying a constant of proportionality or unit rate. They will also apply proportional relationships and ratios to percent problems.

Essential Outcomes of the Unit

Ratios and Proportional Relationships

Analyze proportional relationships and use them to solve real-world and mathematical problems.

• 7.RP.1 Compute unit rates associated with ratios of fractions.
• 7.RP.2 Recognize and represent proportional relationships between quantities.
• 7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Note: Examples of percent problems include: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, and percent error.

Other Standards Addressed in the Unit

Ratios and Proportional Relationships

Analyze proportional relationships and use them to solve real-world and mathematical problems.

• 7.RP.2a Decide whether two quantities are in a proportional relationship.
• 7.RP.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
• 7.RP.2c Represent a proportional relationship using an equation.
• 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.
  

Download the complete Ratios and Proportional Relationships framework to customize for your own planning.

Expressions, Equations and Inequalities 

Students will deepen their understandings of relationships between quantities as they write and simplify expressions, equations, and inequalities that represent real world contexts.  

Note: Lessons will vary in length, depending on the amount of time you have with students, the resources that you choose to accompany the unit, the level of rigor within each learning target, and any other factors that may contribute to the pacing of your learning progressions. It is recommended that you adjust the pace and length of each learning progression(s) accordingly in response to these factors. 

These learning progressions were developed using Next Generation Learning Standards and were crosswalked with the Common Core Standards.  

Download the complete Grade 7 Unit 2 framework to customize for your own planning.

Essential Outcomes

• NY-7.EE.1 : dd, 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.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. e.g., The perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
  • Note: The words leading to in the standard may require students to simplify or combine like terms on the same side of the equation before it is in the form stated in the standard. This standard is a fluency expectation for grade 7. For more guidance, see Fluency in the Glossary of Verbs Associated with the New York State Next Generation Mathematics Learning Standards. 
• NY-7.EE.4b: Solve word problems leading to inequalities of the form px + q > r, px + q ≥ r, px + q ≤ r, or px + q < r, where p, q, and r are rational numbers. Graph the solution set of the inequality on the number line and interpret it in the context of the problem. e.g., As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.
  • Note: The words leading to in the standard may require students to simplify or combine like terms on the same side of the equation before it is in the form stated in the standard.

Essential Questions and Big Ideas

• How do I identify equivalent expressions? 
  • Expressions with the same variable can be combined or subtracted.  
  • Coefficients of like terms can be combined or subtracted.  
• How can I represent percentages mathematically?
  • Percentages can be represented as a decimal to the hundredths.  
  • A percentage multiplied by a variable represents a percentage of that amount.  
• How can I represent areas and perimeters mathematically?
  • Side lengths can be represented using variables.  
  • With a known area or perimeter, a side length can be solved for in an equation. 
• How can I solve real world problems using equations/inequalities?
  • Constants can be moved to the same side of an equation.  
  • When a coefficient with a variable is found to equal a constant, the constant can be divided by the coefficient to find the value of the variable. 

Download the complete Grade 7 Unit 2 framework to customize for your own planning.

The Number System: Rational Numbers

Students will make connections from positive integers to negative integers. Students will connect what they know about addition and subtraction, to add, subtract, multiply, and divide positive and negative numbers. Students will also deepen their understanding of rational numbers.

Essential Outcomes

The Number System

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

Other Standards Addressed in this Unit

The Number System

• 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 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 properties of operations as strategies to add and subtract rational numbers.
• NY-7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide 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.
• 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.

Essential Questions and Big Ideas

• What are integers?
  • Integers are numbers that can be written as whole numbers.
  • Integers can be positive or negative.
• How do I add with positive and negative integers?
  • To add positive integers, combine their values.
  • To add a positive and a negative integer, find the difference between the values. If there is more negative, the answer will be negative. If there is more positive, the answer will be positive.
  • To add two negative integers, combine the value of the integers and it remains negative.
• How do I subtract with positive and negative integers?
  • To subtract positive integers, find the difference between the two. If you’re taking away a larger number, the difference will be negative. If you’re taking away a smaller number, the difference will be positive
  • To subtract a positive number from a negative number, it is the same as adding two negative numbers.
  • Subtracting a negative number means taking away a negative, which is the same as adding a positive.
• How do I multiply with positive and negative integers?
  • Multiplying a positive number by a negative number creates a negative number, as either you are taking away groups of a positive number or combining groups of a negative number.
  • Multiplying a negative number by a negative number creates a positive number, because it represents taking away groups of a negative, and taking away a negative is actually creating a positive.
• How do I divide with positive and negative integers?
  • Dividing a positive number by a negative number or a negative number by a positive number, leads to a negative quotient, because it represents splitting up a negative total into groups or splitting a positive number up into negative groups, which would require the negative groups to be subtracted.
  • Dividing a negative number by a negative number leads to a positive quotient, because it represents splitting a negative total into groups of a negative and identifying how many groups there are.
• What are rational numbers and how do I complete all four operations with them?
  • Rational Numbers are numbers that can be represented as a fraction or a terminating or repeating decimal.
  • Fractions can be converted to decimals by dividing the numerator by the denominator.
  • The integer rules for addition, subtraction, multiplication, and division apply to all rational numbers.

Download the complete Grade 7 Math Unit 1 framework to customize for your own planning.