Learning Targets/Success Criteria: Math 700
Module 3: Expressions and Equations
Priority Standards:
7.EE.A.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
7.EE.A.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, 𝑎 + 0.05𝑎 = 1.05𝑎 means that “increase by 5%” is the same as “multiply by 1.05.”
7.EE.B.3 Solve multi-step real-life 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; and assess the reasonableness of answers using mental computation and estimation strategies. For example: 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 9¾ inches long in the center of a door that is 27½ 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.
7.EE.B.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.
7.G.B.4 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
7.G.B.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure.
7.G.B.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms
Overarching Skills:
Computation with rational numbers
Term
Constant
Coefficient
Variable
Like terms
Factor
Linear expression
Distribute
Equation
Solution
Inequality
Greater than
Less than
Greater than or equal to
Less than or equal to
Angles
Understand/Be able to do:
Topic:
Days: 1
Equivalent Expressions
Eureka Lessons: 1 & 2
Walt:
We are learning to simplify and compare equivalent expressions
Success Criteria:
Topic:
Days: 2 & 3
Combining Like Terms and Distributive Property
Eureka Lessons: 3, 4, 5, & 6
Walt:
We are learning to simplify expressions using the distributive property and combining like terms
Success Criteria:
Topic:
Days: 9
Classifying Angles
Eureka Lessons: 10
Walt:
We are learning to classify angles
Success Criteria:
Topic:
Days: 10, 11 & 12
Solve for missing angles
Eureka Lessons: 10 & 11
Walt:
We are learning to solve for missing angles
Success Criteria:
Topic:
Days: 15 & 16
Solve and Graph Inequalities
Eureka Lessons: 12, 13, 14 & 15
Walt:
We are learning to solve and graph inequalities
Success Criteria:
Topic:
Days: 20, 21 & 22
Area of 2 Dimensional Figures
Eureka Lessons: 16, 17, 18, 19 & 20
Walt:
We are learning to find the area of 2 dimensional figures
Success Criteria:
Topic:
Days: 26, 27, & 28
Surface Area
Eureka Lessons: 21, 22, 25 & 26
Walt:
We are learning to find surface area
Success Criteria:
Topic:
Days: 29, 30, & 31
Volume
Eureka Lessons: 23, 24, 25 & 26
Walt:
Success Criteria:
re to edit.
Module 3: Expressions and Equations
Priority Standards:
7.EE.A.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
7.EE.A.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, 𝑎 + 0.05𝑎 = 1.05𝑎 means that “increase by 5%” is the same as “multiply by 1.05.”
7.EE.B.3 Solve multi-step real-life 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; and assess the reasonableness of answers using mental computation and estimation strategies. For example: 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 9¾ inches long in the center of a door that is 27½ 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.
7.EE.B.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.
- Solve word problems leading to equations of the form 𝑝 + 𝑞 = 𝑟 and 𝑝(𝑥 + 𝑞) = 𝑟, where 𝑝, 𝑞, and 𝑟 are specific 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. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
- Solve word problems leading to inequalities of the form 𝑝 + 𝑞 > 𝑟 or 𝑝 + 𝑞 < 𝑟, where 𝑝, 𝑞, and 𝑟 are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: 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.
7.G.B.4 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
7.G.B.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure.
7.G.B.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms
Overarching Skills:
Computation with rational numbers
- Fractions
- Decimals
- Whole numbers
- Integers
- Multi-step problems
Term
Constant
Coefficient
Variable
Like terms
Factor
Linear expression
Distribute
Equation
Solution
Inequality
Greater than
Less than
Greater than or equal to
Less than or equal to
Angles
- Acute
- Obtuse
- Right
- Straight
- Supplementary
- Complementary
- Vertical
- Adjacent
- Angle Sum Theorem
- Interior angles
- Exterior angles
- Parallelogram
- Triangle
- Trapezoid
- Circle
- Polygon
- Circle
- Rectangular Prism
- Pyramid
- Triangular prism
- Cylinder
- Rectangular Prism
- Triangular Prism
- Pyramid
- Cylinder
Understand/Be able to do:
- Add/Subtract/Multiply/Divide positive and negative rational numbers in any form
- Apply order of operations to simplify numerical expressions
- Simplify linear expressions by combining like terms and distributive property
- Identify equivalent linear expressions
- Write and solve equations to represent real world problems and interpret solutions
- Write, solve, graph, and interpret inequalities to represent real world problems..
- Find the area of a parallelogram/triangle/trapezoid/circle
- Find perimeter of polygons.
- Find the circumference of a circle
- Identify length/base, width, height, radius, diameter
- Calculate radius from diameter
- Find the surface area of a rectangular & triangular prism, pyramid, cylinder.
- Find the volume of a rectangular & triangular prism, pyramid, cylinder.
- Identify acute, right, obtuse, straight angles
- Identify supplementary, complementary, vertical, adjacent angle pairs
- Solve for missing angle measures using equations
- Identify interior and exterior angles
- Apply Angle Sum Theorem to find missing angles in triangles
Topic:
Days: 1
Equivalent Expressions
Eureka Lessons: 1 & 2
Walt:
We are learning to simplify and compare equivalent expressions
Success Criteria:
- I can generate equivalent expressions using the fact that addition and multiplication can be done in any order (commutative property) and any grouping (associative property).
- I can recognize how any order, any grouping can be applied in a subtraction problem by using additive inverse relationships (adding the opposite) to form a sum and likewise with division problems by using the multiplicative inverse relationships (multiplying by the reciprocal) to form a product.
- I can recognize that any order does not apply to expressions mixing addition and multiplication, leading to the need to follow the order of operations.
- I can generate equivalent expressions using the fact that addition and multiplication can be done in any order (commutative property) and any grouping (associative property).
- I can recognize how any order, any grouping can be applied in a subtraction problem by using additive inverse relationships (adding the opposite) to form a sum and likewise with division problems by using the multiplicative inverse relationships (multiplying by the reciprocal) to form a product.
- I can recognize that any order does not apply for expressions mixing addition and multiplication, leading to the need to follow the order of operations.
Topic:
Days: 2 & 3
Combining Like Terms and Distributive Property
Eureka Lessons: 3, 4, 5, & 6
Walt:
We are learning to simplify expressions using the distributive property and combining like terms
Success Criteria:
- I can use area and rectangular array models and the distributive property to write products as sums and sums as products.
- I can use the fact that the opposite of a number is the same as multiplying by −1 to write the opposite of a sum in standard form.
- I can recognize that rewriting an expression in a different form can shed light on the problem and how the quantities in it are related.
- I can use an area model to write products as sums and sums as products.
- I can use the fact that the opposite of a number is the same as multiplying by −1 to write the opposite of a sum in standard form.
- I can recognize that rewriting an expression in a different form can shed light on the problem and how the quantities in it are related.
- I can recognize the identity properties of 0 and 1 and the existence of inverses (opposites and reciprocals) to write equivalent expressions.
- I can rewrite rational number expressions by collecting like terms and combining them by repeated use of the distributive property.
Topic:
Days: 9
Classifying Angles
Eureka Lessons: 10
Walt:
We are learning to classify angles
Success Criteria:
- I can use vertical angles, adjacent angles, angles on a line, and angles at a point in a multistep problem to write and solve simple equations for an unknown angle in a figure.
Topic:
Days: 10, 11 & 12
Solve for missing angles
Eureka Lessons: 10 & 11
Walt:
We are learning to solve for missing angles
Success Criteria:
- I can use vertical angles, adjacent angles, angles on a line, and angles at a point in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
Topic:
Days: 15 & 16
Solve and Graph Inequalities
Eureka Lessons: 12, 13, 14 & 15
Walt:
We are learning to solve and graph inequalities
Success Criteria:
- I can justify the properties of inequalities that are denoted by < (less than), ≤ (less than or equal to), > (greater than), and ≥ (greater than or equal to).
- I can understand that an inequality is a statement that one expression is less than (or equal to) or greater than (or equal to) another expression, such as 2𝑥𝑥 + 3 < 5 or 3𝑥𝑥 + 50 ≥ 100.
- I can interpret a solution to an inequality as a number that makes the inequality true when substituted for the variable.
- I can convert arithmetic inequalities into a new inequality with variables (e.g., 2 × 6 + 3 > 12 to 2𝑚𝑚 + 3 > 12) and give a solution, such as 𝑚𝑚 = 6, to the new inequality. They check to see if different values of the variable make an inequality true or false.
- I can solve word problems leading to inequalities that compare 𝑝𝑝𝑝𝑝 + 𝑞𝑞 and 𝑟𝑟, where 𝑝𝑝, 𝑞𝑞, and 𝑟𝑟 are specific rational numbers.
- I can interpret the solutions in the context of the problem.
- I can graph solutions to inequalities taking care to interpret the solutions in the context of the problem.
Topic:
Days: 20, 21 & 22
Area of 2 Dimensional Figures
Eureka Lessons: 16, 17, 18, 19 & 20
Walt:
We are learning to find the area of 2 dimensional figures
Success Criteria:
- I can develop the definition of a circle using diameter and radius.
- I know that the distance around a circle is called the circumference and discover that the ratio of the circumference to the diameter of a circle is a special number called pi, written 𝜋.
- I know the formula for the circumference 𝐶 of a circle, of diameter 𝑑, and radius 𝑟. I will use scale models to derive these formulas.
- I can use 22/7 and 3.14 as estimates for 𝜋 and informally show that 𝜋 is slightly greater than 3.
- I can give an informal derivation of the relationship between the circumference and area of a circle.
- I know the formula for the area of a circle and can use it to solve problems.
- I can examine the meaning of quarter circle and semicircle.
- I can solve area and perimeter problems for regions made out of rectangles, quarter circles, semicircles, and circles, including solving for unknown lengths when the area or perimeter is given.
- I can find the areas of triangles and simple polygonal regions in the coordinate plane with vertices at grid points by composing into rectangles and decomposing into triangles and quadrilaterals.
- I can find the area of regions in the coordinate plane with polygonal boundaries by decomposing the plane into triangles and quadrilaterals, including regions with polygonal holes.
- I can find composite areas of regions in the coordinate plane by decomposing the plane into familiar figures (triangles, quadrilaterals, circles, semicircles, and quarter circles).
Topic:
Days: 26, 27, & 28
Surface Area
Eureka Lessons: 21, 22, 25 & 26
Walt:
We are learning to find surface area
Success Criteria:
- I can find the surface area of three-dimensional objects whose surface area is composed of triangles and quadrilaterals. They use polyhedron nets to understand that surface area is simply the sum of the area of the lateral faces and the area of the base(s).
- I can solve real-world and mathematical problems involving volume and surface areas of three dimensional objects composed of cubes and right prisms.
Topic:
Days: 29, 30, & 31
Volume
Eureka Lessons: 23, 24, 25 & 26
Walt:
Success Criteria:
- I can use the known formula for the volume of a right rectangular prism (length × width × height).
- I understand the volume of a right prism to be the area of the base times the height.
- I can compute volumes of right prisms involving fractional values for length.
- I can use the formula for the volume of a right rectangular prism to answer questions about the capacity of tanks.
- I can compute volumes of right prisms involving fractional values for length.
- I can solve real-world and mathematical problems involving volume and surface areas of three dimensional objects composed of cubes and right prisms.
re to edit.
What to teach
Topic 1: Solving Equations
- I can balance an equation.
- I can identify the inverse operation.
- I can combine like terms within an equation.
- I can identify when to use the distributive property in an equation.
- I can distribute a whole number, fraction, and decimal.
- I can use the distributive property to simplify an equation.
- I can evaluate an algebraic equation.
Topic 2: Using Equations
- I can interpret the solution of an equation.
- I can write an algebraic equation to represent a scenario.
- I can identify equivalent algebraic equations.
- I can generate equivalent algebraic equations.
- I can identify what a variable represents within scenarios.
Topic 3: Solving Inequalities
- I can balance an inequality.
- I can identify the inverse operation.
- I can combine like terms within an inequality.
- I can identify when to use the distributive property in an inequality.
- I can distribute a whole number, fraction, and decimal.
- I can use the distributive property to simplify an inequality.
- I can evaluate an algebraic inequality.
Topic 4: Using Inequalities
- I can interpret the solution of an inequality.
- I can graph the solution of an inequality.
- I can write an algebraic inequality to represent a scenario.
- I can identify equivalent algebraic inequalities.
- I can generate equivalent algebraic inequalities.
- I can identify what a variable represents within scenarios.
vocabulary
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Unit ResourcesAssessmentPre Assessment
Real World Experience Post Assessment Formative Assessment Student Reflection and Goal Setting Sheet |
Learn the Math |