 ## Formative Assessment and Bridging activities These materials were co-designed by teachers, coaches and math teacher educators and are part of an iterative design process. We continue refine and enhance the resources for teachers. Feedback is welcome and accepted at the link below.
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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 6.1

Standard 6.1 Represent relationship between quantities using ratio, and use appropriate notations such as a/b, a to b, and a:b.

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Understanding the Learning Trajectory

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Big Ideas:

Important Assessment Look Fors:

Purposeful Questions: ### Student Strengths

Students can recognize part to whole relationships and use fractions to represent part to whole relationships.

### Bridging Concepts

Students can find equivalencies for part to whole relationships.

### Standard 6.1

Students can represent relationships between quantities using ratio, and use appropriate notations such as “a to b” a:b and a/b.

Games/Tech:

## Standard 6.2a

Standard 6.2a Represent and determine equivalencies among fractions, mixed numbers, decimals, and percents

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Understanding the Learning Trajectory

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Big Ideas:

Important Assessment Look Fors:

Purposeful Questions: ### Student Strengths

Students can represent and identify equivalencies among fractions and decimals, with and without models.

### Bridging Concepts

Students can understand equivalent relationships and represent and identify equivalencies among fractions and decimals without models.

### Standard 6.2a

Students can represent and determine equivalencies among fractions, mixed numbers, decimals, and percents.

Games/Tech:

## Standard 6.2b

Standard 6.2b- Compare and order postive rational numbers

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Understanding the Learning Progression

Big Ideas:

Important Assessment Look Fors:

Purposeful Questions: ### Student Strengths

Students can compare and order fractions and/or decimals in a given set using models or a computational strategy.

### Bridging Concepts

Students can use multiple strategies to compare and order fractions, mixed numbers, and decimals.

### Standard 6.2b

Students can compare and order positive rational numbers.

## Standard 6.3a

Standard 6.3a Identify and represent integers.

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Understanding the Learning Progression

Big Ideas:

Important Assessment Look Fors:

Purposeful Questions: ### Student Strengths

Students can create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of whole numbers.

### Bridging Concepts

Students can understand values on a number line and modeling with different manipulatives.

### Standard 6.3a

Students can identify and represent integers.

## Standard 6.3b

Standard 6.3b Compare and order integers.

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Understanding the Learning Progression

Big Ideas:

Important Assessment Look-fors:

Purposeful questions: ### Student Strengths

Students can model integers, correctly label a number line, and understand mathematical symbols and use them correctly.

### Bridging Concepts

Students can compare and order integers in ascending or descending order and identify integers represented by a point on a number line.

### Standard 6.3b

Students can compare and order integers with a number line; and compare integers using mathematical symbols.

## Standard 6.3c

Standard 6.3c Identify and describe absolute value of integers.

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Understanding the Learning Progression

Big Ideas:

Important Assessment Look-fors:

Purposeful questions: ### Student Strengths

Students can identify and represent integers.
Students can order and compare integers.

### Bridging Concepts

Students understand that opposite integers are an equal distance from zero.

### Standard 6.3c

Students can identify and describe absolute value of integers.

## Standard 6.4

Standard 6.4 Recognize and represent patterns with whole number exponents and perfect squares.

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Understanding the Learning Progression

Big Ideas:

Important Assessment Look-fors:

Purposeful questions: ### Student Strengths

Students use an array model for multiplication.
Students can determine numerical patterns in a table using addition/subtraction.

### Bridging Concepts

Students can determine numerical patterns in a table using multiplication/division.
Students have whole number multiplication fact fluency.

### Standard 6.4

Students can recognize and represent patterns with whole number exponents and perfect squares.

## Standard 6.5a

Standard 6.5a Multiply and divide fractions and mixed numbers.

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Understanding the Learning Progression

Big Ideas:

Important Assessment Look-fors:

Purposeful questions: ### Student Strengths

Students can solve single step practical problems involving multiplication of a whole number limited to twelve or less and a proper fraction with models.

### Bridging Concepts

Students can simplify fractions, understand how to change mixed fractions to improper fractions and vice versa, and multiply a whole number by a fraction.

### Standard 6.5a

Students can multiply and divide fractions and mixed numbers.

## Standard 6.5B

Standard 6.5b Solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions.

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Understanding the Learning Progression

Big Ideas:

Important Assessment Look-fors:

Purposeful questions: ### Student Strengths

Students can solve single step problems and add and subtract fractions.

### Bridging Concepts

Students can multiply a whole number and a proper fraction. Students can solve multistep problems using whole numbers and/or fractions.

### Standard 6.5b

Students can solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions.

## Standard 6.5C

Standard 6.5c Solve multistep practical problems involving addition, subtraction, multiplication and division of decimals.

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Understanding the Learning Progression

Big Ideas:

Important Assessment Look-fors:

Purposeful questions: ### Student Strengths

Students can create and solve single-step and multistep practical problems involving addition, subtraction of decimals.

### Bridging Concepts

Students can solve multistep practical problems with multiplication of decimals and single-step practical problems involving division of decimals.

### Standard 6.5c

Students can solve multistep practical problems involving addition, subtraction, multiplication and division of decimals.

## Standard 6.6a

Standard 6.6a Add, subtract, multiply, and divide integers

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Understanding the Learning Progression

Big Ideas:

Important Assessment Look-fors:

Purposeful questions: ### Student Strengths

Students can add, subtract, multiply, and divide whole numbers fluently.Students can represent integers on a number line, as well as compare and order integers with and without number lines.

### Bridging Concepts

Students can add, subtract, multiply and divide integers using concrete models.

### Standard 6.6a

Students can add, subtract, multiply, and divide integers.

## Standard 6.6b

Standard 6.6b Solve practical problems involving operations with integers

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Understanding the Learning Progression

Big Ideas:

Important Assessment Look-fors:

Purposeful questions: ### Student Strengths

Students can solve single step practical problems using whole numbers and plot integers on a number line.

### Bridging Concepts

Students can add, subtract, multiply, and divide integers and can recognize vocabulary related to positive or negative change..

### Standard 6.6b

Students can solve practical problems involving operations with integers.

## Standard 6.6c

Standard 6.6c Simplify numerical expressions involving integers.

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Understanding the Learning Progression

Big Ideas:

Important Assessment Look-fors:

Purposeful questions: ### Student Strengths

Students can perform operations with whole numbers.
Students can simplify expressions using order of operations without exponents.

### Bridging Concepts

Students can perform operations using integers.
Students understand that absolute value is the distance from zero.
Students understand that an exponent is repeated multiplication

### Standard 6.6c

Students can simplify numerical expressions involving integers.

## Standard 6.7ab

Standard 6.7ab The student will:

a) derive π (pi);

b) solve problems, including practical problems, involving circumference and area of a circle;

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Understanding the Learning Progression

Big Ideas:

Important Assessment Look-fors:

Purposeful questions: ### Student Strengths

Students can find the area of triangles and rectangles.

### Bridging Concepts

Students understand the relationship between the radius and the diameter.
Students understand that the circumference is approximately 3 times the diameter.

### Standard 6.7ab

Students can a) derive π (pi);b) solve problems, including practical problems, involving circumference and area of a circle;

## Standard 6.7c

Standard 6.7c Solve problems, including practical problems, involving area and perimeter of triangles and rectangles.

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Understanding the Learning Progression

Big Ideas:

Important Assessment Look-fors:

Purposeful questions: ### Student Strengths

Students can find area and perimeter of rectangles using models.
Students can find the perimeter of triangles.

### Bridging Concepts

Students understand and can apply the formulas for finding the area of rectangles and triangles.
Students understand when to find area and when to find perimeter

### Standard 6.7c

Students can solve problems, including practical problems, involving area and perimeter of triangles and rectangles.

## Standard 6.8a

Standard 6.8a Identify the components of the coordinate plane

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Understanding the Learning Progression

Big Ideas:

Important Assessment Look-fors:

Purposeful questions: ### Student Strengths

Students can identify congruent figures and recognize parallel, perpendicular, and intersecting lines.

### Bridging Concepts

Students can identify positive and negative numbers on a horizontal and vertical number line.

### Standard 6.8a

Students can identify the components of the coordinate plane.

## Standard 6.8b

Standard 6.8b Identify the coordinates of a point and graph ordered pairs in a coordinate plane

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Understanding the Learning Progression

Big Ideas:

Important Assessment Look-fors:

Purposeful questions: ### Student Strengths

Students can identify components of the coordinate plane, find the area and perimeter of a rectangle or triangle, and identify congruent figures.

### Bridging Concepts

Students can identify integers on a horizontal and vertical number line.

### Standard 6.8b

Students can identify points in the coordinate plane and graph ordered pairs in the coordinate plane.