## Formative Assessment and Bridging activities

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*These standards are bridging standards. Standards are considered a bridge when they: function as a bridge to which other content within the grade level/course is connected; serve as prerequisite knowledge for content to be addressed in future grade levels/courses; or possess endurance beyond a single unit of instruction within a grade level/course.

## Standard 8.1

Standard 8.1 Compare and order real numbers.

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## UNDERSTANDING THE LEARNING Trajectory

Big Ideas:

Important Assessment Look Fors:

Purposeful Questions:

Student Strengths

Students can represent and determine equivalencies among, and order fractions, mixed numbers, decimals, percents, exponents, perfect squares, and integers. Ordering may be in ascending or descending order.

Bridging Concepts

Students can represent and determine equivalencies square roots and numbers written in scientific notation. Ordering may be in ascending or descending order.

Standard 8.1

Students can compare and order real numbers.

## Standard 8.2

Standard 8.2 Describe the relationships between the subsets of the real number system.

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Understanding the Learning Trajectory

Big Ideas:

Important Assessment Look Fors:

Purposeful Questions:

### Student Strengths

Students can simplify fractions

Students can determine the equivalent representations of rational numbers

Students can determine the value of perfect squares and square roots

### Bridging Concepts

Student can perform operations involving rational numbers

Students can find the absolute value of rational numbers

### Standard 8.2

Students can describe the relationships between the subsets of the real number system.

## Standard 8.3ab

Standard 8.3ab The student will

a) estimate and determine the two consecutive integers between which a square root lies; and

b) determine both the positive and negative square roots of a given perfect square.

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Understanding the Learning Trajectory

Big Ideas:

Important Assessment Look Fors:

Purposeful Questions:

### Student Strengths

Students can identify the perfect squares from 0 to 400.

Students can determine the positive square root of a perfect square from 0 to 400.

### Bridging Concepts

Students can describe the difference between rational and irrational numbers

Students can understand the difference between perfect squares and non-perfect squares.

### Standard 8.3ab

Students can

a) estimate and determine the two consecutive integers between which a square root lies; and

b) determine both the positive and negative square roots of a given perfect square.

## Standard 8.4

Standard 8.4 Solve practical problems involving consumer applications.

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Understanding the Learning Trajectory

Big Ideas:

Important Assessment Look Fors:

Purposeful Questions:

### Student Strengths

Students can problem solve using rational numbers and proportional reasoning.

### Bridging Concepts

Students can find tax, tip and discount, solve problems with similar figures, and practical problems with proportional reasoning..

### Standard 8.4

Students can solve practical problems involving consumer applications.

## Standard 8.5

Standard 8.5 Use relationships among pairs of angles that are vertical angles, adjacent angles, supplementary angles, and complementary angles to determine the measure of unknown angles.

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Understanding the Learning Trajectory

Big Ideas:

Important Assessment Look Fors:

Purposeful Questions:

### Student Strengths

Students can classify and measure right, acute, obtuse, and straight angles.

### Bridging Concepts

Students can use the symbol ≅ to represent congruence and can identify and denote congruent angles with the appropriate markings.

### Standard 8.5

Use relationships among pairs of angles that are vertical angles, adjacent angles, supplementary angles, and complementary angles to determine the measure of unknown angles

## Standard 8.6a

Standard 8.6a Solve problems, including practical problems, involving volume and surface area of cones and square-based pyramids.

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Understanding the Learning Trajectory

Big Ideas:

Important Assessment Look Fors:

Purposeful Questions:

### Student Strengths

Students can evaluate and simplify algebraic expressions

### Bridging Concepts

Students can solve problems, including practical problems, involving volume and surface area of rectangular prisms and right cylinders

### Standard 8.6a

Students can solve problems, including practical problems, involving volume and surface area of cones and square-based pyramids.

## Standard 8.6b

Standard 8.6b Describe how changing one measured attribute of a rectangular prism affects the volume and surface area.

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Understanding the Learning Trajectory

Big Ideas:

Important Assessment Look Fors:

Purposeful Questions:

### Student Strengths

Students can describe and determine the surface area and volume of a rectangular prism.

### Bridging Concepts

Students can make connections between the scale factor of the lengths of similar prisms and the corresponding scale factor of the volumes of these similar figures.

### Standard 8.6b

Students can describe how changing one measured attribute of a rectangular prism affects the volume and surface area.

### Routines:

• Good Questions for Math Techers page 256

## Standard 8.7ab

Standard 8.7ab The student will:

a) Given a polygon, apply transformations, to include translations, reflections, and dilations, in the coordinate plane; and

b) Identify practical applications of transformations.

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Understanding the Learning Trajectory

Big Ideas:

Important Assessment Look Fors:

Purposeful Questions:

### Student Strengths

Students can identify ordered pairs  in the coordinate plane

Students can graph ordered pairs in the coordinate plane

### Bridging Concepts

Students can perform translations of quadrilaterals and right triangles in the coordinate plane
Students can perform reflections over the x-axis or the y-axis in the coordinate plane.

### Standard 8.7ab

Students can

a) given a polygon, apply transformations, to include translations, reflections, and dilations, in the coordinate plane; and

b) identify practical applications of transformations.

## Standard 8.8

Standard 8.8 Construct a three-dimensional model, given the top or bottom, side, and front views.

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Understanding the Learning Trajectory

Big Ideas:

Important Assessment Look Fors:

Purposeful Questions:

### Student Strengths

Students can describe, compare and contrast solid figures based on their characteristics.

### Bridging Concepts

Students can identify solid figures based on characteristics, pictorial representations or concrete models.

### Standard 8.8

Students can construct a three-dimensional model, given the top or bottom, side, and front views.

## Standard 8.9a

Standard 8.9a Verify the Pythagorean Theorem.

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Understanding the Learning Trajectory

Big Ideas:

Important Assessment Look Fors:

Purposeful Questions:

### Student Strengths

Recognize and represent patterns with whole number exponents and perfect squares.

Students can identify the perfect squares from 0 to 400.

Students can determine the positive square root of a perfect square from 0 to 400.

Students can estimate and determine the two consecutive integers between which a square root lies.

### Bridging Concepts

Students can identify perfect squares and estimate non-perfect squares.
Students understand how to create an area model of a square given the length of one side.

### Standard 8.9a

Students can verify the Pythagorean Theorem.

## Standard 8.9b

Standard 8.9b Apply the Pythagorean Theorem.

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Understanding the Learning Trajectory

Big Ideas:

Important Assessment Look Fors:

Purposeful Questions:

### Student Strengths

Students can identify the perfect squares from 0 to 400 and determine the positive square root of a perfect square from 0 to 400.

### Bridging Concepts

Students can determine the positive or negative square root of a given perfect square from 1 to 400. They can verify the Pythagorean Theorem, using diagrams, concrete materials, and measurement.

### Standard 8.9b

Apply the Pythagorean Theorem

## Standard 8.10

Standard 8.10 Solve area and perimeter problems, including practical problems, involving composite plane figures.

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Understanding the Learning Trajectory

Big Ideas:

Important Assessment Look Fors:

Purposeful Questions:

### Student Strengths

Students can derive an approximation for pi (3.14 or 22/7) by gathering data and comparing the circumference to the diameter of various circles, using concrete materials or computer models.

They can solve problems involving circumference and area of a circle when given the length of the diameter or radius.

They can solve problems involving area and perimeter of triangles and rectangles.

### Bridging Concepts

Students can solve practical problems involving circumference and area of a circle when given the length of the diameter or radius. They can solve practical problems involving area and perimeter of triangles and rectangles.

### Standard 8.10

Students can solve area and perimeter problems, including practical problems, involving composite plane figures.

## Standard 8.11a

Standard 8.11a Compare and contrast the probability of independent and dependent event.

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Understanding the Learning Trajectory

Big Ideas:

Important Assessment Look Fors:

Purposeful Questions:

### Student Strengths

Students can determine the theoretical and experimental probabilities of an event.

### Bridging Concepts

Students can describe changes in the experimental probability as the number of trials increases.
Students can investigate and describe the difference between the probability of an event found through experiment or simulation versus the theoretical probability of that same event.

### Standard 8.11a

Students can determine whether two events are independent or dependent. Students can compare and contrast the probability of independent and dependent events.

## Standard 8.11b

Standard 8.11b Determine the probabilities for independent and dependent events.

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Understanding the Learning Trajectory

Big Ideas:

Important Assessment Look Fors:

Purposeful Questions:

### Student Strengths

Students can describe changes in the experimental probability as the number of trials increases. Investigate and describe the difference between the probability of an event found through experiment or simulation versus the theoretical probability of that same event.

### Bridging Concepts

Students can determine whether two events are independent or dependent. Students can compare and contrast the probability of independent and dependent events.

### Standard 8.11b

Students can determine the probability of two independent or dependent events.

## Standard 8.12abc

Standard 8.12abc The student will:

a) Represent numerical data in boxplots;

b) Make observations and inferences about data represented in boxplots; and

c) Compare and analyze two data sets using boxplots.

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Understanding the Learning Trajectory

Big Ideas:

Important Assessment Look Fors:

Purposeful Questions:

### Student Strengths

Students can organize data in a line plot, stem-and-leaf-plot, and circle graph.

Students can identify measures of central tendency.

Students can identify the range of data as a measure of spread

### Bridging Concepts

Students can make observations and inferences about the same data presented in different graphical representations.

### Standard 8.12abc

Students can

a) represent numerical data in boxplots;

b) make observations and inferences about data represented in boxplots; and

c) compare and analyze two data sets using boxplots.

## Standard 8.13ab

Standard 8.13ab The student will:

a) Represent data in scatterplots;

b) Make observations about data represented in scatterplots;

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Understanding the Learning Trajectory

Big Ideas:

Important Assessment Look Fors:

Purposeful Questions:

### Student Strengths

Students can plot an ordered pair in the coordinate plane.

Students can organize data using a line plot, stem-and-leaf plot, circle graph or histogram

### Bridging Concepts

Students can make inferences and observations regarding data presented in various graphical forms.
Students can determine which value is the independent and the dependent variables given bi-variable data.

### Standard 8.13ab

Students can

a) represent data in scatterplots;

b) make observations about data represented in scatterplots;

## Standard 8.13c

Standard 8.13c Use a drawing to estimate the line of best fit for data represented in a scatterplot.

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Understanding the Learning Trajectory

Big Ideas:

Important Assessment Look Fors:

Purposeful Questions:

### Student Strengths

Students can plot ordered pairs in all four quadrants of the coordinate plane.

Students can graph a linear function in y=mx form or y=x+b form.

### Bridging Concepts

Students can make connections between relationships of two quantities using tables, graphs, verbal descriptions and equations.
Students can graph a linear equation in y=mx+b form.

### Standard 8.13c

Students can use a drawing to estimate the line of best fit for data represented in a scatterplot.