Middle School Math
Boynton and DeWitt middle schools utilize a heterogeneous math model in grades six and seven. Both schools offer Algebra I and Math 8 for students in eighth grade. Below are resources to support students and families:
Course Decisions
All course options, grades 6-8:
Math Learning Standards
While all learning standards are important in seventh-grade math, the curriculum has been divided into six priority content-standard categories that help us determine a student’s eighth-grade placement.
Students will have multiple in-class opportunities during their seventh-grade year to demonstrate proficiency in the priority standard categories.
Students who score a minimum of level 3 in the six priority areas and score at least two areas at level 4 will be recommended for Algebra and Algebra Companion.
Students who do not meet this requirement will be placed in Math 8.
If an interested student does not meet the Algebra criteria, they can review over the summer and take a placement test in August. Students who meet the qualifications for algebra with this assessment will not have an opportunity to test out of algebra the companion course.
Priority Seventh Grade Content Standards
Category One: Ratios and Proportional Reasoning
Analyze proportional relationships and use them to solve real-world and mathematical problems
Standards | Description |
|---|---|
NY-7.RP 1 | Compute unit rates associated with ratios of fractions |
NY-7.RP 2 a, b, c, & d | Recognize and represent proportional relationships between quantities |
Category Two: Percent
Solve a wide variety of percent problems including, for example, simple interest, tax, markups and markdowns, percent increase and decrease, and percent error
Standards | Description |
|---|---|
NY-7.RP 3 | Use proportional relationships to solve multistep ratio and percent problems |
Category Three: Integer Operations
Interpret and apply the rules for adding, subtracting, multiplying, and dividing with positive and negative numbers
Standards | Description |
|---|---|
NY-7.NS 1 a, b, c, & d | Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers. Represent addition on a horizontal or vertical number line |
NY-7.NS 3 | Solve real-world and mathematical problems involving the four operations with rational numbers |
Category Four: Rational Numbers
Broaden understandings of the number system to include positive and negative rational numbers and work with fractions to solve real-world problems
Standards | Description |
|---|---|
NY-7.NS 2 a, b, c, & d | Apply and extend previous understanding of multiplication and division of fractions to multiply and divide rational numbers. |
NY-7.NS 3 | Solve real-world and mathematical problems involving the four operations with rational numbers |
Category Five: Expressions
Use properties of operations to generate equivalent expressions
Standards | Description |
|---|---|
NY-7.EE 1 | Add, subtract, factor, and expand linear expressions with rational coefficients by applying the properties of operations |
NY-7.EE 2 | Understand that rewriting an expression in different forms in real-world and mathematical problems can reveal and explain how the quantities are related. |
Category Six: Equations
Solve real-life and mathematical problems using numerical and algebraic expressions, equations, and inequalities
Standards | Description |
|---|---|
NY-7.EE 3 | Solve multi-step real-world and mathematical problems posed with positive and negative rational numbers in any form using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate. Assess the reasonableness of answers using mental computation and estimation strategies. |
NY-7.EE 4 a & b | 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. |
Algebra Companion Course
If an eighth grader would like to take Algebra I, they will need to take a companion course to ensure that they have a solid foundation in eighth-grade concepts. You may also test out of the companion course.
The companion course can be taken during the summer, during the school day, before or after school.
Standards | Description |
|---|---|
NY-7.EE 3 | Solve multi-step real-world and mathematical problems posed with positive and negative rational numbers in any form using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate. Assess the reasonableness of answers using mental computation and estimation strategies. |
NY-7.EE 4 a & b | 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. |
NY-8.EE 7 A & B | Solve linear equations in one variable. |
NY-8.EF 2 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). |
NY-8.EF 4 | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. |
NY-8.G 1 A, B, & C | Verify experimentally the properties of rotations, reflections, and translations. |
NY-8.G 2 | Know that a two-dimensional figure is congruent to another if the corresponding angles are congruent and the corresponding sides are congruent. Equivalently, two two-dimensional figures are congruent if one is the image of the other after a sequence of rotations, reflections, and translations. Given two congruent figures, describe a sequence that maps the congruence between them on the coordinate plane. |
NY-8.G 3 | Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. |
NY-8.G 4 | Know that a two-dimensional figure is similar to another if the corresponding angles are congruent and the corresponding sides are in proportion. Equivalently, two, two-dimensional figures are similar if one is the image of the other after a sequence of rotations, reflections, translations, and dilations. Given two similar two-dimensional figures, describe a sequence that maps the similarity between them on the coordinate plane. |
NY-8.G 5 | Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. |
NY-8.G 6 | Understand a proof of the Pythagorean Theorem and its converse. |
NY-8.G 7 | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. |
NY-8.G 8 | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. |
NY-8.G 9 | Given the formulas for the volume of cones, cylinders, and spheres, solve mathematical and real-world problems. |
NY-8.EE 3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. |
NY-8.EE 3 | Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. |
NY-8.EE 4 | Perform multiplication and division with numbers expressed in scientific notation, including problems where both standard decimal form and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Interpret scientific notation that has been generated by technology. |