**St. Paul Catholic School Math Expectations**

The teaching faculty at St. Paul Catholic School worked diligently reviewing their teaching practices in mathematics, researching instructional best practices, examining the Common Core Standards for Math, and collaborating on the development of a school-wide math continuum that reflects the school’s expectations for all students. The resulting document, the St. Paul Catholic School Math Expectations, embraces the notion that our students will not only have math-based content knowledge but also the ability to apply and infuse that knowledge across disciplines and in a variety of problem-solving situations.

Parents play a key role in every child’s development. This role is not limited to that which takes place at home in the areas of spiritual, social, emotional, physical and educational development of their child but includes that of expending and reinforcing the efforts of the school and its faculty and staff. Therefore, parents are a major component and an extension of the teaching and learning that happens at St. Paul Catholic School and as such are viewed as partners in their child’s educational and spiritual development. The math continuum is designed to inform parents of the school’s expectations at each grade level and to encourage parents to have conversations with their children about the learning that is taking place at school. Parents are expected to provide feedback to their child’s teacher on the progress their child is making in math and to actively engage in home-based activities and efforts which support and extend the learning that occurs in the classroom. It is through such a collaboration that the potential for student growth and development is maximized. Parents are asked to review, not only the math expectations for their child’s grade level but also the expectations of the previous and next grade levels as well to better understand the flow and sequence of the school’s math curriculum.

**Kindergarten Math Expectations**

Students enter kindergarten at various stages of development. Some can read, write, and compute at a beginning level while others are still exploring the world of print and computation. With this in mind, the Kindergarten curriculum is designed to meet each student at their level of performance while supporting and continuing the growth and development that encompasses the individual child as well as the classroom community as a whole.

Therefore, students in Kindergarten are presented with skills, concepts, operations and processes that include but are not limited to the following:

**Counting and whole numbers:**developing a proficiency in counting and comparing whole numbers.**Operations and Algebraic Thinking:**developing an understanding of addition, subtraction, and strategies for solving addition and subtraction problems to 10.**Number and Operations in Base Ten:**developing an understanding of number relationships and place value.**Measurement and Data:**developing an understanding of measuring and comparing objects.**Geometry:**developing a proficiency in identifying 2-dimensional and 3-dimensional shapes.

**In addition to prior knowledge, students completing Kindergarten are expected to demonstrate the following math skills, concepts, operations and processes by being able to:**

**Counting and Whole Numbers**

- Count independently to 100 by ones and tens.
- Write and identify numbers 0-20
- Use ordinal numbers (1st-31st) while reading the date on a calendar, providing and receiving directions, and in describing objects.
- Count objects to 20 (giving each object a number)
- Count objects to 20 (how many objects total?)
- Compare number of objects (up to 10 objects)
- Compare numbers 1-10 (identifying which number is higher, lower, or the same)

**Operations and Algebraic Thinking**

- Represent addition and subtraction with objects, fingers, images, drawings, acting out situations, and written equations to 10
- Fluently add and subtract to 5 independently
- Decompose numbers to 10 (such as 5= 2+3 and 5= 4+1)
- Compose numbers to 10 (5+? = 10; 4+? = 10)

**Numbers and Operations in Base Ten**

- Compose and decompose numbers from 11 to 19 into one group of 10 and some further ones. (such as 18 = 10 + 8)

**Measurement and Data**

- Describe measurable several measurable attributes of a single object (big, small, tall, short, etc.) using their length, weight, or height.
- Compare two objects (taller/ shorter, larger/smaller)
- Classify, sort, and count objects by their attributes (size, shape, color, etc.)

**Geometry** (2D shapes: squares, circles, triangles, rectangles, trapezoid, hexagons; 3D shapes: cubes, cones, cylinders, spheres)

- Describe objects in the environment using names of shapes listed above and position words such as above, below, beside, in front of, behind, and next to
- Correctly name the shapes listed above.
- Identify the listed shapes as 2D or “flat” or 3D “solid”
- Analyze and compare 2D and 3D shapes using words such as vertices, corners, sides, etc.
- Model, build, and draw each of the listed shapes.
- Compose larger shapes from simple shapes (two triangles form a rectangle, two triangles and a square form a trapezoid, etc.) Students should be able to create a square, rectangle, trapezoid, and hexagon.

**Grade 1 Math Expectations**

Students in Grade 1 have experienced at least a full year of formalized math instruction in a learning environment. As such, each child has been exposed to the relationship between a numeral representation and the number concept for that numeral as well as learning several basic math operations and processes for manipulating and applying numbers and computations.

Therefore, students in Grade 1 are presented with skills, concepts, operations and processes that include but are not limited to the following:

**Operations and Algebraic Thinking:**developing an understanding of addition, subtraction, and strategies for solving addition and subtraction problems beyond 10.**Measurement and Data:**developing a continuing understanding of measuring and comparing objects including the concept of time.**Money:**developing understanding of the values of coins and using that knowledge in addition and subtraction operations**Geometry:**developing a greater proficiency in identifying 2-dimensional and 3-dimensional shapes and understanding the concept of symmetry.

**In addition to prior knowledge, students completing Grade 1 are expected to demonstrate the following math skills, concepts, operations and processes by being able to:**

**Operations and Algebraic Thinking**

- Represent and solve problems involving addition and subtraction. Ex: 6+5=11 and 9-6=3
- Understand & apply properties of operations and the relationship between addition/subtraction. Ex: If 8+3=11 is known, then 3+8=11 is also known.
- Add and subtract to 20 and be able to solve word problems to the sum of 20. Ex. 13+7=20 and 20-4=16
- Work with addition and subtraction equations. Ex: 7=8-1 or 5+2=2+5
- Numbers and Operations in Base Ten
- Expand the counting sequence. Ex. 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120.
- Understand place value – Ones, tens, Hundreds and know what a bundle of ten is.
- Use place value understanding and properties of operations to add and subtract without carrying. The sum of the problem will not exceed the number 20. Ex: 10+10=20

**Measurement and Data**

- Measure lengths indirectly by iterating length units. Ex: Order three objects by length
- Tell and write time on the hour and half hour
- Represent and interpret data. Ex. Reading and filling in a chart, picture graph, or a bar graph

**Money**

- Know the values of the coins and be able to add the coins together and find the sum.

**Geometry**

- Reason with shapes and their attributes. Ex: know that triangles are closed figures and they are a three-sided shape.
- Know what symmetry is and how to represent the line of symmetry with a shape or figure.

**Know Vocabulary Words**

In addition to the math vocabulary learned in kindergarten the first graders will need to know the following words…

Digit, addends , addition, subtract, subtraction, sum, numeral, difference, greater than, less than, equal, ones, tens, hundreds, place value, symbol, analog clock, digital clock, data, graph, length, measure, longer, shorter, cube, cone, cylinder, rectangular prism, trapezoid, triangle, square, rectangle, circle, shape, three-dimensional shape

**Grade 2 Math Expectations**

Students in Grade 2 have begun to formalize their basic math operations and processes and can manipulate and apply these skills in basic computation. In Grade 2, instructional time focuses on four critical areas: extending understanding of base-ten notation; building fluency with addition and subtraction; using standard units of measure; and describing and analyzing shapes. It is the level at which addition and subtraction of multiple numbers is reinforced and the concepts relating to such are extended to pre-multiplication applications in Grade 3.

Therefore, students in Grade 2 are presented with skills, concepts, operations and processes that include but are not limited to the following:

**Operations and Algebraic Thinking:**developing an understanding of addition, subtraction, and strategies for solving addition and subtraction problems within 20 while working with equal groups of objects to gain foundations for multiplication**Number Operations in Base Ten:**developing an understanding of place value and using that understanding in addition and subtraction**Measurement and Data:**developing and applying estimation in standard units to help solve problems; the applying addition and subtraction to money and time; and learning how to represent and interpret data.**Geometry:**developing a greater proficiency with multi-dimensional objects and the concept of reason with shapes and their attributes

**In addition to prior knowledge, students completing Grade 2 are expected to demonstrate the following math skills, concepts, operations and processes by being able to:**

**Operations and Algebraic Thinking**

- Use addition to develop fluency with addition and subtraction within 100
- Solve problems within 1000 by applying an understanding of models for addition and subtraction, and they develop, discuss, and use efficient, accurate, and generalizable methods to compute sums and differences of whole numbers in base-ten notation, using their understanding of place value and the properties of operations.
- Select and accurately apply methods that are appropriate for the context and the numbers involved to mentally calculate sums and differences for numbers with only tens or only hundreds.
- Represent and solve problems involving addition and subtraction.
- Add and subtract within 20.
- Manipulate equal groups of objects to gain foundations for multiplication.

**Number and Operations in Base Ten**

- Understand the base-ten system. This includes ideas of counting in fives, tens, and multiples of hundreds, tens, and ones, as well as number relationships involving these units, including comparing.
- Understand multi-digit numbers (up to 1000) written in base-ten notation, recognizing that the digits in each place represent amounts of thousands, hundreds, tens, or ones (e.g., 853 is 8 hundreds + 5 tens + 3 ones).
- Understand place value.
- Use place value understanding and properties of operations to add and subtract.

**Measurement and Data**

- Recognize the need for standard units of measure (centimeter and inch) and use rulers and other measurement tools with the understanding that linear measure involves an iteration of units.
- Recognize that the smaller the unit, the more iterations they need to cover a given length.
- Measure and estimate lengths in standard units
- Relate addition and subtraction to length
- Work with time and money as values
- Represent and interpret data

**Geometry**

- Reason with shapes and their attributes
- Describe and analyze shapes by examining their sides and angles.
- Investigate, describe, and reason about decomposing and combining shapes to make other shapes.
- Develop a foundation for understanding area, volume, congruence, similarity, and symmetry in later grades through building, drawing, and analyzing two- and three-dimensional shapes

**Grade 3 Math Expectations**

In math, Grade 3 is a pivotal year as instructional time moves away from an emphasis on addition and subtract toward more complex operations in four critical areas: developing an understanding of multiplication and division and strategies for multiplication and division within 100; developing an understanding of fractions, especially unit fractions (fractions with numerator 1); developing an understanding of the structure of rectangular arrays and of area; and describing and analyzing two-dimensional shapes.

Therefore, students in Grade 3 are presented with skills, concepts, operations and processes that include but are not limited to the following:

**Operations and Algebraic Thinking:**

- Representing and solving problems involving multiplication and division.
- Understanding the properties of multiplication and the relationship between multiplication and division.
- Multiplying and dividing within 100.
- Solving problems involving the four operations (Addition, Subtraction, Multiplication, and Division), and identify and explain patterns in arithmetic.

**Number and Operations in Base Ten**

- Using place value understanding and properties of operations to perform multi-digit arithmetic.

**Number and Operations—Fractions**

- Developing an understanding of fractions as numbers.

**Measurement and Data**

- Solving problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
- Representing and interpreting data.

**Geometric measurement:**

- Understanding the concepts of area and relate area to multiplication and to addition.
- Recognizing the perimeter as an attribute of plane figures and distinguishing between linear and area measures.

**Geometry:**

- Reasoning with shapes and their attributes.

**In addition to prior knowledge, students completing Grade 3 are expected to demonstrate the following math skills, concepts, operations and processes by being able to:**

**Operations and Algebraic Thinking** (Operations and thinking processes related to the relationship between numbers.)

- Represent and solve word problems involving multiplication and division within 100.
- Understand properties of multiplication and the relationship between multiplication and division.
- Multiply and divide within 100.
- Solve number and word problems involving the four operations (addition, subtraction, multiplication and division) and identify and explain the patterns of arithmetic.

**Number and Operations in Base Ten** (The use of operations when working with whole numbers and their place values.)

- Use place value understanding and properties of operations to perform multi-digit arithmetic to 1000.

**Number and Operations – Fractions** (The use of operations when working with fractions.)

- Develop understanding of fractions as numbers. Add and subtract equivalent fractions with like denominators.
- Compare 2 fractions with the same denominator.

**Measurement and Data** (The use of operations with measurement and numerical data.)

- Solve problems involving measurement and estimation of intervals of time to the minute and elapsed time, liquid volumes, and masses of objects.
- Represent and interpret date; create/produce picture.
- Understand concepts of area and relate area to multiplication and addition with squares and rectangles by using geometric measurement.
- Recognize perimeter as an attribute of plane figures and polygons, and distinguish between linear and area measures.
- Use geometric measurement with halves and fourths of an inch.

**Geometry** (The understanding of shapes, lines and angles.)

- Reason with shapes and their attributes (rhombus, rectangles, quadrilaterals and others).

**Grade 4 Math Expectations**

In Grade 4, instructional time will focus on three critical areas: developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends; developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry. This year, the instruction increases the student’s level of exploration of both multiplication and division and examines both shapes and fractions and the relationship of part-to-whole.

Therefore, students in Grade 4 are presented with skills, concepts, operations and processes that include but are not limited to the following:

**Operations and Algebraic Thinking:**

- Using the four operations (Addition, Subtraction, Multiplication, and Division) with whole numbers to solve problems.
- Gaining familiarity with factors and multiples.
- Generating and analyzing patterns.

**Number and Operations in Base Ten:**

- Generalizing place value understanding for multi-digit whole numbers.
- Using place value understanding and properties of operations to perform multi-digit arithmetic.

**Number and Operations—Fractions:**

- Extending understanding of fraction equivalence and ordering.
- Building fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
- Understanding decimal notation for fractions, and comparing decimal fractions.

**Measurement and Data:**

- Solving problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
- Representing and interpreting data.
- Understanding concepts of angle and measure angles by using geometric measurement.

**Geometry:**

- Drawing and identifying lines and angles, and classifying shapes by properties of their lines and angles.

**In addition to prior knowledge, students completing Grade 4 are expected to demonstrate the following math skills, concepts, operations and processes by being able to:**

**Operations and Algebraic Thinking Operations** (The thinking processes related to the relationships between numbers).

- Use the four operations (addition, subtraction, multiplication and division) to solve number and word problems with whole numbers.
- Solve problems by using a single step or operation, or using up to three-step operations.
- Determine factors and multiples for numbers 1-100.
- Recognize, continue or create number patterns using one rule (ex. +3, x2, -10).
- Continue a given pattern series when given a table of values with inputs or outputs missing.

**Number and Operations in Base Ten** (The use of operations when working with whole numbers and their place values).

- Identify and apply place value understanding for multi-digit whole numbers up to 1,000,000.
- Name the place in problems such as naming the place of the 5 in 845,621 or the 3 in 237,186.
- Use place value and operations to perform multi-digit arithmetic using the four mathematical operations.
- Solve addition and subtraction problems involving multi-digit numbers 0 -1,000,000.
- Solve multiplication problems that include the multiplication of a single-digit number and multi-digit number with up to 3 digits (124 x 5) and the multiplication of two 2-digit numbers (24 x 37).
- Solve division problems that include the division of a single-, two- or three-digit number by a single digit number, and those division problems resulting in a single digit remainder.

**Number and Operations – Fractions** (The use of operations when working with fractions).

- Explain why two fractions with different numerators and denominators are equivalent, using visual models such as (1/2 = 2/4).
- Create equivalent fractions through multiplication of a fraction equal to 1.
- Compare fractions with different numerators and denominators by using visual models and creating a common denominator using their knowledge of factors and multiples.
- Use understanding of addition and subtraction to add and subtract fractions with the same denominator.
- Add and subtract mixed numbers with the same denominator by using equivalent fractions or visual models to solve.
- Use understanding of multiplication to multiply fractions by a whole number, using visual models, repeated addition and multiplication to solve.
- Solve word problems involving addition, subtraction and multiplication of fractions that have the same denominator and refer to the same whole by using visual models and equations to represent and solve the problem.
- Write a fraction with the denominator of 10 as an equivalent fraction with a denominator of 100 such as (6/10 = 60/100)
- Add two fractions with related denominators (3/10 + 40/100 = 70/100).
- Use decimal notation for fractions with denominators of 10 or 100.
- Compare two decimals to the hundredths place by reasoning about their size and using understanding of place value.
- Record the result of a comparison using >, =, or < symbols and justify their conclusion using visual models.

**Measurement and Data** (The use of operations with measurement and numerical data).

- Know the relative size of measurement units in the Metric and US Customary systems to measure length, mass/weight, capacity/volume and time.

Metric units: mm, cm, m, km; g, kg; ml, l

US Customary units: in, ft, yd, mi; oz, lb; fl oz, cup, quart, pint, gallon

Time units: sec, min, hour - Within a single measurement system, convert between smaller and larger units and record measurement equivalents in a two-column table.
- Use the four operations (Addition, Subtraction, Multiplication and Division) to solve word problems involving measurement and the conversion of measurements from a larger unit to a smaller unit.
- Apply the area and perimeter formulas for rectangles in real world and mathematical problems.
- Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8).
- Solve problems involving addition and subtraction of fractions using information presented in line plots.
- Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand the following concepts of angle measurement:
- Measure an angle with reference to a circle with its center at the common endpoint of two rays.
- Measure an angle that turns 1/360 of a circle and is called a “one-degree angle”.
- Know that an angle measurement is equal to the number of one-degree angles it is equivalent to.
- Measure angles in whole-number degrees using a protractor and sketch angles of a given angle measure.
- Recognize that angle measure is additive and that an angle measure is equal to the sum of its parts.
- Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems using an equation with a symbol for the unknown angle measure.

**Geometry** (The understanding of shapes, lines and angles)

- Draw lines (perpendicular and parallel), line segments, rays, and angles (right, acute, obtuse) and identify these in two-dimensional figures.
- Classify two-dimensional shapes by properties of their lines and angles:
- presence or absence of parallel or perpendicular lines
- presence or absence of angles of a specified size

- Recognize right triangles as a category of two-dimensional figures and identify them.
- Recognize a line of symmetry for a two-dimensional figure as a line across the figure that if the figure were folded along this line, the two parts would match.
- Identify and draw lines of symmetry for given two-dimensional figures.

**Grade 5 Math Expectations**

In Grade 5, instructional time focuses on three critical areas: Students continue to develop fluency with addition and subtraction of fractions. In addition, they develop an understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions). Division is extended to two digit divisors, integrating decimal fractions into the place value system and developing an understanding of operations with decimals to hundredths. Students develop fluency with whole number and decimal operations. Volume is introduced as an attribute of three-dimensional space. They understand that volume can be measured by finding the total number of same-size units of volume required to fill the space without gaps or overlaps.

Therefore, students in Grade 5 are presented with skills, concepts, operations and processes that include but are not limited to the following:

**Operations and Algebraic Thinking**

- Writing and interpreting numerical expressions.
- Analyzing patterns and relationships.

**Number and Operations in Base Ten**

- Understanding the place value system.
- Performing operations with multi-digit whole numbers and with decimals to hundredths.

**Number and Operations—Fractions**

- Using equivalent fractions as a strategy to add and subtract fractions.
- Appling and extending previous understandings of multiplication and division to multiply and divide fractions.

**Measurement and Data**

- Converting like measurement units within a given measurement system.
- Representing and interpreting data.
- Understanding concepts of volume and relating volume to multiplication and to addition using geometric measurement.

**Geometry**

- Graphing points on the coordinate plane to solve real-world and mathematical problems.
- Classifying two-dimensional figures into categories based on their properties.

**In addition to prior knowledge, students completing Grade 5 are expected to demonstrate the following math skills, concepts, operations and processes by being able to:**

**Operations and Algebraic Thinking**

- Write and interpret numerical expressions. This standard calls for students to evaluate expressions with parentheses, brackets, and braces. Expressions are a series of numbers and symbols (+, -, x, /) without an equals sign.
- Analyze patterns and relationships. Students are given two rules and generate two numerical patterns. The graphs that are created should be line graphs to represent the pattern.

**Number and Operations in Base Ten**

- Understand the place value system. This standard calls for students to reason about the magnitude of the numbers. Students should work with the idea that the tens place is ten times as much as the ones place, and the ones place is 1/10th the size of the tens place.
- Perform operations with multi-digit whole numbers and decimals to hundredths. Students continue work on division, extending it to computation of whole number quotients with dividends of up to four digits and two-digit divisors.

**Number and Operations – Fractions**

- Use equivalent fractions as a strategy to add and subtract fractions. Students should apply their understanding of equivalent fractions and their ability to rewrite fractions in an equivalent form to find common denominators.
- Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Students connect fractions with division, understanding that 5 divided by 3 = 5/3. Students can explain why the procedures for multiplying and dividing fractions make sense. This is limited to the case of dividing unit fractions by whole numbers and whole numbers by unit fractions.

**Measurement and Data**

- Convert like measurement units within a given measurement system. Students can convert 5 cm to 0.05m and use these conversions in solving multi-step, real world problems.
- Represent and interpret data. Students use operations on fractions for this grade to solve problems involving information presented in line plots.
- Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. This standard involves finding the volume of right rectangular prisms. Students should have experiences to describe and reason about why the formula is true. That they are covering the bottom of a right rectangular prism (length x width) with multiple layers (height)

**Geometry**

- Graph points on the coordinate plane to solve real world and mathematical problems. This standard deals with only the first quadrant (positive numbers) in the coordinate plane.
- Classify two dimensional figures into categories based on their properties. Students understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.

**Grade 6 Math Expectations**

In Grade 6, instructional time focuses on four critical areas: Students connecting ratio and rate to whole number multiplication and division using concepts of ratio and rate to solve problems. They complete their understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers. Students can write, interpret, and use expressions and equations. Students develop an understanding of statistical thinking.

Therefore, students in Grade 6 are presented with skills, concepts, operations and processes that include but are not limited to the following:

**Ratios and Proportional Relationships**

- Understanding ratio concepts and using ratio reasoning to solve problems.

**The Number System**

- Applying and extending previous understandings of multiplication and division to divide fractions by fractions.
- Multiplying and dividing multi-digit numbers and find common factors and multiples.
- Applying and extending previous understandings of numbers to the system of rational numbers.

**Expressions and Equations**

- Applying and extending previous understandings of arithmetic to algebraic expressions.
- Reasoning about and solve one-variable equations and inequalities.
- Representing and analyzing quantitative relationships between dependent and independent variables.

**Geometry**

- Solving real-world and mathematical problems involving area, surface area, and volume.

**Statistics and Probability**

- Developing an understanding of statistical variability.
- Summarizing and describing distributions.

**In addition to prior knowledge, students completing Grade 6 are expected to demonstrate the following math skills, concepts, operations and processes by being able to:**

**Ratios and Proportional Relationships**

- Understand ratio concepts and use ratio reasoning to solve problems. This standard calls for students to use reasoning about multiplication and division to solve ratio and rate problems about quantities.
- Solve a wide variety of problems involving ratios and rates.

**The Number System**

- Apply and extend previous understandings of multiplication and division to divide fractions by fractions. Students are able to divide a whole number by a fraction. Students can divide a fraction by a fraction by using its reciprocal.
- Compute fluently with multi-digit numbers and find common factors and multiples. Students can use the standard algorithms of each operation. Students can find the greatest common factor of two whole numbers less than or equal to 100.
- Apply and extend previous understandings of numbers to the system of rational numbers. Students can use rational numbers (fractions, decimals, and integers) to represent real-world situations.

**Expressions and Equations**

- Apply and extend previous understandings of arithmetic to algebraic expressions. Students write expressions from verbal descriptions using letters and numbers. Example: Express the cost of renting the Roller Dome ($25) and the admission fee ($5) per student.
- Reason about and solve one variable equations and inequalities. Students explore equations as expressions being set equal to a specific value. The solution is the value of the variable that will make the equation or inequality true. Students use inspection to solve the equation.
- Represent and analyze quantitative relationships between dependent and independent variables. The cost of gasoline per gallon is $3.50. What will the cost of gasoline be for a 100 mile trip?

**Geometry (G)**

- Solve real life and mathematical problems involving area, surface area, and volume. Students are able to find the area of a rectangle and a triangle.
- Decompose shapes into rectangle and triangles to determine the area.
- Find the surface area of rectangular prism and triangular prism and the volume of a rectangular prism.

**Statistics and Probability**

- Develop understanding of statistical variability.
- Display data using dot plots, histograms, and box plots.

**Summarize and Describe Distributions**

- Select and analyze the measures of central tendency (mean, median, and mode), or variability to represent and summarize a data set for the purposes of answering questions.

**Grade 7 Math Expectations**

In Grade 7, instructional time focuses on four critical areas: Students develop an understanding of and applying proportional relationships. They also develop an understanding of operations with rational numbers and working with expressions and linear equations. Students solve problems involving scale drawings and informal geometric constructions. They work with two and three dimensional shapes to solve problems involving area, surface area, and volume. Students can draw inferences about populations based on samples.

Therefore, students in Grade 7 are presented with skills, concepts, operations and processes that include but are not limited to the following:

**Ratios and Proportional Relationships**

- Analyzing proportional relationships and using them to solve real-world and mathematical problems.

**The Number System**

- Applying and extending previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

**Expressions and Equations**

- Using properties of operations to generate equivalent expressions.
- Solving real-life and mathematical problems using numerical and algebraic expressions and equations.

**Geometry**

- Drawing, constructing and describing geometrical figures and describe the relationships between them.
- Solving real-life and mathematical problems involving angle measure, area, surface area, and volume.

**Statistics and Probability**

- Using random sampling to draw inferences about a population.
- Drawing informal comparative inferences about two populations.
- Investigating chance processes and developing, using, and evaluating probability models

**In addition to prior knowledge, students completing Grade 7 are expected to demonstrate the following math skills, concepts, operations and processes by being able to**:

**Ratios and Proportional Relationships**

- Analyze proportional relationships and use them to solve real world and mathematical problems. Students continue their work for 6th grade but now include fractions compared to fractions.
- Use an understanding of proportional reasoning to solve problems that are easier to solve with cross- multiplication.

**The Number System**

- Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. (This includes integers)

**Expressions and Equations**

- Use properties of operations to generate equivalent expressions. Students can combine like terms,
- Solve real life and mathematical problems using numerical and algebraic expressions and equations.
- Solve problems using rational numbers.
- Convert between fractions, decimals, and percents as needed to solve problems.

**Geometry**

- Draw, construct, and describe geometrical figures and describe the relationships between them.
- Determine the dimensions of figures when given a scale and identify the impact of a scale on actual length, or area.
- Solve real life and mathematical problems involving angle measure, area, surface area, and volume.
- Use formulas for the area and circumference of circle to solve problems.
- Continue work from previous grades on solving area and volume problems.

**Statistics and Probability**

- Use random sampling to draw inferences about a population.
- Recognize that a sampling can be used to represent a total population.
- Draw informal comparative inferences about two populations.
- Use samples to make comparisons within a certain population. Compare medians, ranges
- Investigate chance processes and develop, use, and evaluate probability models. This is the first formal introduction of probability.
- Collect data from a probability experiment.
- Focus on relative frequency.

**Grade 8 Math Expectations**

In Grade 8, instructional time focuses on three critical areas: Students can formulate and reason about expressions and equations (including modeling an association in bi-variate data with a linear equation), and solving linear equations and systems of linear equations. Students grasp the concept of a function and the use of functions to describe quantitative relationships. Students can analyze two and three dimensional space figures using distance, angle, similarity, and congruence. Students understand and can apply the Pythagorean Theorem to real world situations.

Therefore, students in Grade 8 are presented with skills, concepts, operations and processes that include but are not limited to the following:

**The Number System**

- Knowing that there are numbers that are not rational, and approximating them by rational numbers.

**Expressions and Equations**

- Working with radicals and integer exponents.
- Understanding the connections between proportional relationships, lines, and linear equations.
- Analyzing and solving linear equations and pairs of simultaneous linear equations.

**Functions**

- Defining, evaluating, and comparing functions.
- Using functions to model relationships between quantities.

**Geometry**

- Understanding congruence and similarity using physical models, transparencies, or geometry software.
- Understanding and applying the Pythagorean Theorem.
- Solving real-world and mathematical problems involving volume of cylinders, cones and spheres.

**Statistics and Probability**

- Investigating patterns of association in bi-variate data

**In addition to prior knowledge, students completing Grade 8 are expected to demonstrate the following math skills, concepts, operations and processes by being able to:**

**The Number System**

- Know that there are numbers that are not rational, and approximate them by rational numbers.
- Know the elements of Real Numbers.
- Distinguish between rational and irrational numbers.

**Expressions and Equations**

- Work with radicals and integer exponents. Integer (positive and negative) exponents are further developed to generate equivalent numerical expressions when multiplying, dividing, or raising a power to a power.
- Use scientific notation to describe very large or very small numbers.
- Understand the connections between proportional relationships, lines, and linear equations.
- Use the slope of a line to describe a unit rate.
- Analyze and solve linear equations and pairs of simultaneous linear equations.
- Solve equations with variables on both sides.

**Functions**

- Define, evaluate, and compare functions.
- Understand rules that take x as input and gives y as output. Students identify functions from equations, graphs, and tables.
- Use functions to model relationships between quantities.
- Understand that the equation represents the relationship between the x-value and the y-value.
- Determine the rate of change

**Geometry**

- Understand congruence and similarity using physical models, transparencies, or geometry software.
- Use tools or technology to explore figures created from translations, reflections, and rotations.
- Understand and apply the Pythagorean Theorem.
- Explain a proof of the Pythagorean Theorem and its converse.
- Apply the Pythagorean Theorem to determine an unknown side of a right triangle in a real world situation.
- Solve real world and mathematical problems involving volume of cylinders, cones, and spheres.
- Build on knowledge from 7th grade to find volume of cylinders by finding the area of the base and multiplying by the number of layers.

**Statistics and Probability**

- Investigate patterns of association in bivariate data. Bivariate data refers to two-variable data, one to be graphed on the x-axis and the other on the y-axis.
- Represent numerical data on a scatter plot to examine relationships between variables.
- Analyze scatter plots to determine if the relationship is linear or non-linear.