Math Grade 7 PJMS
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15 Days |
Unit 1: Ratios and Proportional Relationships |
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1. What is the constant of proportionality? 2. How can two quantities be identified as proportional or non-proportional? 3. How can the constant of proportionality (unit rate) be determined given a table? Graph? Equation? Diagram? Verbal description? 4. What does a specific point on a graph (x,y) represent? |
Day 1: An experience in relationships as measuring rates Day 2: Proportional relationships Day 3 and Day 4: Identifying proportional and non-proportional relationships in tables Day 5 and Day 6: Identifying propotional and non-proportional relationships in graphs/pre-requisite; graphing on the coordinate plane Day 7: Unit rate as a constant of proportionality Day 8: Unit 1: Quiz 1 Day 9 and Day 10: Representing proportional relationships in equations Day 11 and Day 12: Interpreting graphs of proportional relationships Day 13: Unit 1 Review Day 14 and Day 15: Unit 1 Test
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Ratios Equilvalent ratios Unit Rate Porportional Relationship Constant of Proportionality Complex Fraction Slope |
Students compute unit rates associated with ratios of quantities measured in different units. Students use the context of the problem to recall the meaning of value of a ratio, equivalent ratios, rate and unit rate, relating them to the context of the experience.
Students understand that two quantities are proportional to each other when there exists a constant(number) such that each measure in the first quantity multiplied by this constant gives the corresponding measure in the second quantity.
When students identify the measures in the first quantity with x and the measures in the second quantity with 𝑦, they will recognize that the second quantity is proportional to the first quantity if 𝑦 = 𝑘𝑥 for some positive number 𝑘. They apply this same relationship when using variable choices other than 𝑥 and 𝑦.
Students examine situations to decide whether two quantities are proportional to each other by checking for a constant multiple between measures of x and measures y of when given in a table. Students study examples of relationships that are not proportional in addition to those that are.
Students examine situations carefully to decide whether two quantities are proportional to each other by graphing on a coordinate plane and observing whether all the points would fall on a line that passes through the origin.
Students study examples of relationships that are not proportional as well as those that are.
Students identify the same value relating the measures of x and the measures of y in a proportional relationship as the constant of proportionality and recognize it as the unit rate in the context of a given situation.
Students find and interpret the constant of proportionality within the contexts of problems.
Students use the constant of proportionality to represent proportional relationships by equations in real world contexts as they relate the equations to a corresponding ratio table and/or graphical representation.
Students consolidate their understanding of equations representing proportional relationships as they interpret what points on the graph of a proportional relationship mean in terms of the situation or context of the problem, including the point (0,0).
Students are able to identify and interpret in context the point (1,r) on the graph of a proportional relationship where r is the unit rate. |
Ratios and Unit Rate Worksheet:
Proportional or non-proportional in tables worksheet:
Constant of proportionality in graphs worksheet:
Constant of proportionality as equations worksheet:
Creating tables and graphs worksheet:
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Online assessments |
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15 Days |
Unit 2: Rational Numbers |
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1. How can operations with integers be illustrated in multiple ways? (Models, verbally, and symbolically)
2. What's the difference between the opposite and the absolute value of a number? |
Day 1: Absolute values and integers Day 2: Adding integers Day 3: Subtracting integers Day 4: Multiplying and dividing integers Day 5: Mixed operations with integers Day 6: Unit 2: Quiz 1 Day 7: Converting decimal to fraction, fraction to decimal Day 8: Adding and subtracting fractions Day 9: Adding and subtracting mixed numbers Day 10: Multiplying and dividing fractions Day 11: Dividing complex fractions Day 12: Decimal operations Day 13: Review Day 14: Test
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Integer Absolute Value Whole Numbers Natural Numbers Rational Numbers Additive Inverse Irrational Numbers Additive Inverse Property Commutative Property Product Terminating Decimal Repeating Decimal Multiplicative Inverse Reciprocal
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Students will solve real-world and mathematical problems involving the four operations with rational numbers
Students will apply and extend previous understandings of addition to add rational numbers; represent addition on a horizontal or vertical number line diagram
Students will solve real-world and mathematical problems involving subtraction of integers
Students will apply and extend previous understandings of multiplication of rational numbers, apply properties of operations as strategies to multiply rational numbers, solve real world and mathematical problems involving x with rational numbers
Students will apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
Students will convert a rational number to a decimal using long division and know that the decimal form of a rational number terminates in zeros or eventually repeats.
Students will compare and order rational numbers.
Students will add and subtract rational numbers.
Students will add and subtract mixed numbers.
Students will multiply and divide fractions, mixed numbers, and decimals. |
Converting decimal to fraction, fraction to decimal
Adding and subtracting fractions
Multiplying and dividing fractions
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Online Assessment |
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12 Days |
Unit 3: Expressions |
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How can the properties of rational numbers be used to create equivalent expressions? |
Day 1: Evaluating algebraic and numerical expressions Day 2: Translating and writing algebraic expressions Day 3: Properties of Operations Day 4: Simplifying expressions by combining like terms Day 5: Simplifying expressions using the distributive property Day 6: Quiz Day 7: Adding linear expressions Day 8: Subtracting linear expressions Day 9: Factoring linear expressions Day 10: Review for Test Days 11 and 12: Unit 3 Test |
Numerical Expressions Algebraic Expression Algebra Coefficient Variable Evaluate Order of operations Constant Terms Like terms Linear expression Distributive property
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Students will be able to evaluate numerical and algebraic expressions
Students will translate (write) algebraic expressions
Students will apply properties of operations as strategies to add, subtract, multiply and divide rational numbers
Students will simplify expressions by combining like terms and using the distributive property
Students will add and subtract linear expressions
Students will find the greatest common factor and factor linear expressions
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Evaluationg algebraic expressions
Translating and writing algebraic expressions
Combining like terms and the distributive property
Adding and subtracting linear expressions
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Online Assessment |
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15 Days |
Unit 4: Equations |
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How can estimation be used to test the reasonableness of a solution?
How can the properties of rational numbers be used to create equivalent equations?
How can we use inverse operations to solve a multi-step equation? |
Day 1 and Day 2: Solving one step equations Day 3: Solving one step equations with rational coefficients Day 4: Solving two step equations Day 5 and Day 6: Solving multi-step equations using the distributive property and combining like terms Day 7: Quiz Day 8 and Day 9: Creating and solving number word problems Day 10 and Day 11: Creating and solving real-world word problems Day 12: Testing solutions Day 13: Unit 4 Review Day 14 and Day 15: Unit 4 Test
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Associative property Additive identity property Multiplicative identity property Equation Monomial Consecutive Solution Factor Isolate |
Students will solve one-step equations with rational coefficients
Students will solve two-step equations
Students will solve multi-step equations using the distributive property and combining like terms with rational coefficients
Students will contsruct and solve equations from word problems
Students will determine if a solution to a linear equation is correct or incorrect |
Solving one step equations with rational numbers
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Online assessment |
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10 Days |
Unit 5: Inequalities |
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How can resonalbleness be used to test the solution to an inequality?
How can we use inverse operations to solve multi-step inequalities?
How can the properties of rational numbers be used to create equivalent inequalities?
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Day 1: Introduction to inequalities Day 2: Solving one-step inequalities with addition and subtraction Day 3: Solving one-step inequalities with multiplication and division Day 4: Solving two-step inequalities Day 5 and Day 6: Solving multi-step inequalities using the distributive property and combining like terms with rational coefficients Day 7 and Day 8: Applications of inequalities Day 9: Unit 5 Review Day 10: Unit 5 Test |
Inequality Soltuion set Greater than Less than Greater than or equal to Less than or equal to Inverse operations At least |
Students will graph and translate inequalities
Students will solve and graph one-step inequalities with addition and subtraction
Students will solve and graph one-step inequalities with multiplication and division
Students will solve and graph two-step inequalities
Students will solve multi-step inequalities using the distributive property and combining like terms with rational coefficients
Students will create and solve inequalities from word problems and analyze the solution |
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Online assessment |
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10 Days |
Unit 6: Circles |
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What is the relationship between the area and circumference of a circle? |
Day 1: Understanding circles Day 2: Circumference of a circle Day 3: Area of a circle Day 4: Working backwards- given the circumference, find the diameter and/or the radius Day 5: Area of a shaded region Day 6 and Day 7: Applications of circumference and area of circles Day 8: Unit 6 Review Day 9 and Day 10: Unit 6 Test |
Circle Pi Circumference Area Diameter Radius Chord Center Central angle Sector |
Students will know the formulas for circumference of a circle and use the formula to solve problems
Students will know the formula for area of a circle and use the formula to solve problems
Students will use the circumference formula to work backwards; given the circumference they will find the radius and/or diameter
Students will use the area formulas to calculate the area of a shaded region
Students will know the formulas for area and circumference of a circle and use them to solve word problems and interpret the solutions |
Circumferences and areas of circles
Circumference and areas of circles (2)
Given area and circumference, find the diameter and radius
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Online assessment |
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15 Days |
Unit 7: Percents |
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How can proportions be used to solve real-world problems involving percents? (Mark-up, discounts, tips, tax, and commission)
How can estimation be used to test the reasonableness of a solution? |
Day 1: Investigating Percents Day 2: Working with bar models to find the "whole" Day 3: Percent Proportion Day 4: Percent Equation Day 5: Quiz Day 6: Percent Error Day 7: Commission, Sales Tax, Tips/Gratuities Day 8: Discount and Markup Day 9: Simple Interest Day 10, Day 11, and Day 12: NYS Percent Applications Day 13: Unit 7 Review Day 14 and Day 15: Unit 7 Test
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Percent Percentage Percent Increase Percent Decrease Percent of Change Tax Tip/Gratuity Markup/Markdown Discount Sale Price Commission Fees Simple Interest Percent Error Enlargement Reduction
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Students will use proportional relationships to solve multi-step ratio and percent problems.
Students will write and use the percent equation to answer questions involving percents.
Students will use percentages to solve problems involving percent of change.
Students will use percentages to solve problems involving percent error.
Students will use proportional relationships to solve multistep ratio and percent problems involving commission, sales tax, tips/gratuities.
Students will use percentages to solve problems involving markup and discount (markdown).
Students will use percentages to solve problems involving simple interest.
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Percents to decimals to fractions
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Online Assessment |
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10 Days |
Unit 8: Probability |
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How can a model be used to predict the probability of an event occurring?
How can you determine if a game of chance is fair? |
Day 1: Probability of Simple Events Day 2: Theoretical and Experimental Probability Day 3: Probability and Tree Diagrams Day 4: Fundamental Counting Principal Day 5: Quiz Day 6: Probability of Dependent Events Day 7: Probability of Independent Events Day 8: Stations and Simulations Day 9: Unit 8 Review Day 10 and Day 11: Unit 8 Test |
Probability Theoretical Probability Experimental Probability Simple Events Compound Events Certain Events Impossible Events Sample Space Simulation Tree Diagram |
Students will find the probability of simple events.
Students will explore experimental and theoretical probabilities in games of chance.
Students will use tree diagrams to represent sample spaces for compound events.
Students will find the probability of compound events by applying the fundamental counting principal.
Students will find the probability of independent and dependent events.
Students will design and use a simulation to generate frequencies for compound events. |
Probability of simple, dependent, independent
Fundamental counting principal and sample space
Theoretical and experimental probability
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Online Assessment |
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10 Days |
Unit 9: Statistics |
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How can random sampling be used to draw inferences about a population?
How can data sets be used to predict future events? |
Day 1: Understanding Population Samples Day 2: Measures of Central Tendency Day 3: Measures of Variation Day 4: Quiz Day 5: Drawing Inferences From Data Day 6: Comparing Box Plots Day 7: Comparing Dot Plots Day 8: Unit 9 Review Day 9 and Day 10: Unit 9 Test |
Statistics Inference Random Sample Population Line Plot Box Plot Measures of Center Mean Median Mode Range Maximum Minimum Outlier Upper Quartile Lower Quartile |
Students will understand that statistics can be used to gain information about a population by examining a sample that is representative of the population.
Students will calculate measures of central tendency and describe a set of data using the measures of central tendency of mean, median, and mode.
Students will use measures of center and measures of variability for numerical data.
Students will create and answer questions about box and dot plots.
Students will use data from a random samples to draw inferences about a population with an unknown characteristic of interest.
Students will compare populations using a double box plot and a double dot plot.
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Understanding population samples
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Online Assessment |
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4 Days |
Unit 10: Scale Drawings |
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How can we use proportions to solve problems involving scale drawings and conversions? |
Day 1: Creating and Using Scale Drawings Day 2: Scale Drawings and Constant of Proportionality Day 3: Using the Garde 7 Mathematics Reference Sheet: Answer questions involving conversions between units and scale drawings Day 4: Quiz |
Scale Drawing Proportion Scale Factor Reduction Enlargement Pre-image Image Costant of Proportionality |
Students will create and use scale drawings.
Students understand that a scale drawing is either the reduction or the enlargement of a two-dimensional picture.
Students compare the scale drawing picture with the original picture and determine if the scale drawing is a reduction or an enlargement.
Students match points and figures in one picture with points and figures in the other picture.
Students use the Grade 7 Mathematics Reference Sheet to answer questions involving conversions of different units. |
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Online Assessment |
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8 Days |
Unit 11: Constructions |
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How can we determine whether 3 side lengths will make a triangle?
What are some real-world applications involving area?
How do we classify triangle by their angles? By their sides? |
Day 1: Characteristics of Geometric Shapes Day 2: Naming Angles and Calibrating the Protractor Day 3: Measuring Angles With a Protractor Day 4: Drawing Geometric Shapes Day 5: Area of Two-Dimensional Figures Day 6: Unit 11 Review Day 7 and Day 8: Unit 11 Test |
Polygon Congruent Quadrilateral Triangle Acute Obtuse Right Isoceles Scalene Equilateral Protractor Trapezoid |
Students will classify and draw geometric shapes with given conditions.
Students will name and calibrate angles with a protractor.
Students will measure angles with a protractor.
Students will draw geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
Students will solve real-world mathematical problems involving area of two-dimensional shapes. |
Measuring angles with a protractor
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Online Assessment |
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8 Days |
Unit 12: Angle Relationships |
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How can we solve for an unknown angle?
How can classifying angles help in creating multi-step equations to solve for unknown angles? |
Day 1: Review Angle Relationship Terms Day 2: Complementary and Supplementary Angles Day 3: Vertical and Adjacent Angles Day 4 and Day 5: Creating and Solving Equations for Unknown Angles Day 6: Unit 12 Review Day 7 and Day 8: Unit 12 Test |
Acute Angle Obtuse Angle Right Angle Straight Angle Supplementary Angles Complementary Angles Vertical Angles Adjacent Angles Parallel Lines Intersecting Lines Perpendicular Lines |
Students will 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.
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Online Assessment |
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12 Days |
Unit 13: Surface Area and Volume of 3D Figures |
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How is the area of a 2-dimensional figure related to the volume of a 3-dimensional figure?
What are some real world applications involving volume? |
Day 1: Understanding 3-D Shapes Day 2: Surface Area of Rectangular Prisms and Cubes Day 3: Surface Area of Right Triangular Prisms Day 4 and Day 5: Surface Area of Irregular Figures Day 6: Volume of Rectangular Prisms and Right Triangular Prisms Day 7: Volume of Irregular Figures Day 8: Slicing Geometric Shapes Day 9: Describing Plan Sections Day 10: Unit 13 Review Day 11 and Day 12: Unit 13 Test |
Three-Dimensional Figure Prism Pyramid Surface Area Volume Edge Vertice Face Cross Sections |
Students will solve problems involving three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
Students will calculate surface area and volume of recrangular prisms, cubes, right triangular prisms, and irregular figures.
Students will describe the two-dimensional figures that result from slicing three-dimensional figures as in plane sections of right rectangular prisms and pyramids.
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Surface area of trianglar and rectangular prisms
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Online Assessment |
