Integrated Math
D64 transitions to Integrated Math in 2019-20
As announced in fall 2018, Maine Township High School District 207 is introducing Integrated Math in the 2019-20 school year. Because District 64 offers high school level courses to our advanced middle school students, our course offerings for Accelerated Math and Channels of Challenge math will also include Integrated Math beginning in the 2019-20 school year, too.
As we transition to this new curriculum, this webpage is intended to share: details about the program; tips for parents to support your child at home; and the anticipated trimester schedule of key topics. As we move through this first year of implementation, we will continue to add resources to this webpage.
What is Integrated Math?
Traditionally, high school mathematics in the United States has been taught in the sequence of Algebra 1, Geometry, and Algebra 2. Integrated mathematics re-imagines these courses as Math 1, Math 2, and Math 3, where algebraic, geometric, and statistical thinking are embedded throughout all three courses. Spiraling concepts in this way supports the continued practice of mathematical skills and concepts to help embed them in long-term memory.
After three years of Integrated Math, students will have mastered the concepts presented in a traditional three-year pathway. However, we expect students’ problem-solving and reasoning skills to be much stronger, because Integrated Math more deeply explores the relationships among algebraic, geometric, and statistical concepts. Through the Integrated Math curriculum, students are challenged to solve “math tasks” rather than simply focusing on mastering algorithms.
How have D64 teachers prepared for the transition?
District 64 teachers began preparation for this course during the 2018-19 school year. In collaboration with District 207 teachers, our teachers attended training in the fall of 2018 presented by the curriculum writers of the Mathematics Vision Project, the core resource we will use. In addition to meeting over the course of 2018-19 year, teachers met during the summer to finalize unit plans and will continue to collaborate this school year. Collaboration with the District 207 Math Department will also continue.
How will this impact District 64 offerings?
In District 64, some students enroll in high school level math classes through an accelerated math course sequence. Because District 64’s math sequence aligns with District 207, 7th grade Channels of Challenge students and 8th grade Accelerated Math students will transition to Math 1 in 2019-20. Current 8th grade Channels of Challenge students will complete Algebra II. Beginning in 2020-21, 8th grade Channels of Challenge students will participate in Math 2.
To best prepare students for this coursework, we have adjusted the learning targets and resources used in our current course sequence for Channels of Challenge Math and Accelerated Math. Our former resources for Pre-Algebra and Algebra did not support student mastery of learning targets needed for the integrated math courses (i.e., geometry including rotations, reflections, transformations, 2-D, 3-D; functions). In addition to better aligning with future courses, the adjusted sequence has the added benefit of creating an accelerated experience at grade 6 (previously an enriched course) where students explore advanced topics.
The adjusted course sequence includes the use of the following resources:
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6th Grade |
7th Grade |
8th Grade |
9th Grade |
|---|---|---|---|---|
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Grade Level Pathway |
Course 1 |
Course 2 |
Course 3 |
Integrated Math I |
|
Accelerated Pathway |
Course 2 (formerly Course 1 Enriched) |
Course 3 (formerly Pre-Algebra) |
Integrated Math I (formerly Algebra I) |
Integrated Math II |
|
Channels of Challenge Pathway |
Course 3 (formerly Pre-Algebra) |
Integrated Math I (formerly Algebra I) |
Integrated Math II (beginning in 2020-21 school year) |
Integrated Math III |
What happens after students complete the required 3-year high school math sequence?
After completing three years of high school math, in either the middle school and/or high school setting, all students have the opportunity to participate in “traditional” fourth year courses in District 207 including: PreCalculus, Discrete math (dual credit), AP Calculus AB/BC, Multivariable Calculus, and AP Statistics.
What is the structure of an Integrated Math lesson?
In District 64, as well as in District 207, the integrated math program uses the Mathematics Vision Project as a core resource. As defined by the Mathematics Vision Project, lessons have a unique structure:
- Classroom Experience: During the classroom experience, students are actively engaged in solving a mathematical task. The task has been carefully designed to help your child deepen and connect key mathematical concepts. After students have grappled with a task, they participate in a teacher-facilitated discussion with classmates and share their problem-solving strategies. The teacher facilitates this discussion by highlighting student work. Student thinking is shared, valued, and respected.
- Ready, Set, Go! Homework Assignment: Following each classroom experience, your child will be assigned a Ready, Set, Go! homework assignment. These assignments have been correlated aligned to the daily classroom experience. Beginning in fall 2019, all District 64 Math I students will have access to online help videos to assist with homework. More information about this subscription will be shared with your child at the start of the school year.
How can I best support my child in Integrated Math I?
- Support your child’s teacher by valuing the classroom experience: Discuss the classroom task at home and ask your child to explain his or her thinking.
- Encourage your child to fully participate in the classroom task by thinking “out-of-the box”, asking questions, viewing mistakes as learning opportunities, and contributing to classroom discussions.
- If your student needs help, check that he or she is taking notes on the focus of the lesson and contact your child’s teacher if you are concerned.
- Remind your child about the Ready, Set, Go! homework help subscription (i.e., Homework Help videos).
District 64 and Maine Township High School District 207 hosted a unique, joint presentation (VIEW HERE) on Wednesday, October 17, 2018 regarding the introduction of Integrated Math beginning in the 2019-20 school year.
For more information about Integrated Math in District 207, please see this webpage.
Key ideas and essential questions of Integrated Math I may be viewed by trimester below.
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Key Idea |
Essential Questions |
|---|---|
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Defining quantities and interpreting expressions |
How can variables and mathematical expressions be used to show different ways of seeing a pattern? |
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Representing arithmetic sequences with equations, tables, graphs, and story context |
How can we use mathematical representations to model a pattern? |
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Representing geometric sequences with equations, tables, graphs, and story context |
How can tables and graphs help in writing recursive and explicit formulas? |
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Arithmetic Sequences: Constant difference between consecutive terms, initial values |
How are explicit formulas different than recursive formulas? What are the advantages of using an explicit formula vs a recursive formula? |
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Geometric Sequences: Constant ratio between consecutive terms, initial values |
How are the recursive formulas for geometric and arithmetic sequences alike? How are they different? How are the explicit formulas for geometric and arithmetic sequences alike? How are they different? |
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Arithmetic Sequences: Constant difference between consecutive terms, initial values |
Can an arithmetic sequence be decreasing? |
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Comparing rates of growth in arithmetic and geometric sequences |
What type of sequence grows faster? |
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Recursive and explicit equations for arithmetic and geometric sequences |
How can we efficiently use the information in a table to write formulas for arithmetic and geometric sequences? |
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Using rate of change to find missing terms in an arithmetic sequence |
How can I find missing terms in an arithmetic sequence? |
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Using a constant ratio to find missing terms in a geometric sequence |
How can I find missing terms in an arithmetic sequence? |
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Developing fluency with geometric and arithmetic sequence |
What conclusions can be drawn about a sequence, given just a few pieces of information? |
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Introducing continuous linear and exponential functions |
What are the differences between discrete and continuous functions? Linear and exponential functions? |
|
Connecting context with domain and distinctions between discrete and continuous functions |
How can we determine if the model for a functions should be discrete or continuous? |
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Distinguishing between linear and exponential functions using various representations |
How can I tell if a function is linear or exponential, given any representation? |
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Comparing growth of linear and exponential models |
What type of function increases faster-- linear or exponential? |
|
Interpreting equations that model linear and exponential functions |
Are there different forms for writing equations of lines? What does each form tell us? |
|
Building fluency and efficiency in working with linear and exponential functions in their various forms |
What is the purpose of having different forms of equations? |
|
Calculating and interpreting the average rate of change of a function in a given interval |
How can I find the average rate of change of a function? What does the average rate of change mean? |
|
Using a story context to graph and describe key features of functions |
How do I describe key features of a graph? |
|
Using tables and graphs to interpret key features of functions |
How do I describe key features of a function? |
|
Working to achieve fluency with the identification of features of functions from various representations |
How do I interpret key features of a function? |
|
Interpreting functions and their notation |
What new understanding of features of functions emerge as a result of doing this task? |
|
Combining functions and analyzing contexts using functions |
How do I combine functions graphically and algebraically? |
|
Using graphs to solve problems when given function notation |
Explain why the x-coordinates of the points where the graphs of the equations y=f(x) and y=g(x) intersect are the solutions of the equation f(x)=g(x)? |
|
Identify whether or not a relation is a function given various representations |
When is a relationship also a function? |
|
Matching stories, graphs and equations to assess how well you can connect features from across representations |
How does each representation highlight key features and how can features be used to assist in matching functions given in various representations? |
|
Key Idea |
Essential Questions |
|---|---|
|
Explaining each step in the process of solving an equation |
How does the structure of an equation give me clues about how to solve it? |
|
Rearranging formulas to solve for a variable |
What does it mean to solve an equation that contains multiple variables? How can I use descriptions and units associated with variables to guide my thinking about solving such equations? |
|
Solving literal equations |
How is solving an equation with one variable similar to the work of solving an equation with more than one variable? |
|
Reasoning about inequalities and the properties of inequalities |
What are the properties of inequalities? Why are they different than properties of equations? |
|
Applying the properties of inequalities to solve inequalities |
How can inequalities be used to find solutions to real problem situations? |
|
Solving linear inequalities and representing the solution |
What are some of the misconceptions of inequalities? |
|
Representing constraints with systems of inequalities (introduction) |
How can I represent all possible solutions to a situation that is limited in different ways by various resources or constraints? |
|
Writing and graphing linear inequalities in two variables |
How can I find the complete set of points that satisfy a given constraint? |
|
Writing and solving equations in two variables |
Why is it useful to use equivalent forms of linear equations, and how do I convert a linear equation from one form to the other? |
|
Writing and graphing inequalities in two variables to represent constraints |
What are efficient ways to write the inequalities and sketch the solution sets representing these additional constraints on feeding time and pampering time? |
|
Graphing the solution set to a linear system of inequalities |
How do I represent the points that satisfy all of the constraints on a context? |
|
Solving systems of linear inequalities and representing their boundaries |
How do I interpret inequality signs when determining what to shade as a solution set to an inequality? |
|
Solving systems of linear equations in two variables |
What strategies might I use to find the point of intersection of two linear constraints? |
|
Solving systems of linear equations by elimination (introduction) |
How can I use logical reasoning to solve for two unknown values when I am given two pieces of information about those values? |
|
Solving systems of linear equations by elimination |
How do I use the logical reasoning for solving the scenarios in the previous task when the scenarios are represented with linear equations in standard form? |
|
Working with systems of linear equations, including inconsistent and dependent systems |
Do all systems of linear equations have a solution? Can a system of linear equations have more than one solution? What features of a context help me think about the nature of a solution? |
|
Key Idea |
Essential Questions |
|---|---|
|
Developing the key features of a translation, a rotation, and a reflection? |
How do I create a rigid-motion transformation (translation, rotation or reflection) of a given geometric figure? |
|
Creating the logic of the slope rule for perpendicular lines using rotations |
How can I determine if two lines in a coordinate plane are perpendicular? |
|
Describing a series of transformations that moves the pre-image to the final image including writing equation of a line of reflection, center of rotations, and measure of angles. |
How do I identify a transformation that has already occurred? |
|
Writing and applying formal definitions of the rigid motion transformations. Part 1: Define each of the rigid motion transformations. Part 2: How two reflections can make a rotation |
What can I add to the words slide, flip and turn to more precisely define the rigid-motion transformations-translation reflection and rotation? |
|
Exploring lines of reflection, centers and angles of rotation for rectangles, parallelograms, rhombi, squares, and trapezoids |
What does it mean to say a figure is symmetrical? |
|
Rotational symmetry (finding pattern or formulae) (Vocabulary: line of symmetry, carried only itself, rotational symmetry, diagonal of a polygon, angle, and center of rotation) |
What is "regular" about regular polygons, and how do those features help me flind lines of symmetry and angles of rotational symmetry? |
|
Defining properties of parallelograms, rectangles, squares, and rhombi and the converse of the property using symmetry transformations. |
What observations can i make about different types of quadrilaterals based on their lines of symmetry and rotational symmetry? |
|
Using context to describe data distributions and compare statistical representations |
What information does a histogram tell me? A box plot? |
|
Describing data distributions and compare two or more data sets |
How do I compare two or more data sets based on the statistics appropriate to the shape of the data distribution? |
|
Interpreting two way frequency tables |
What information does a two way table reveal? |
|
Using context to interpret and write conditional statements using relative frequency tables |
What information is highlighted when data is interpreted from relative frequency tables? |
|
Developing an understanding of the value of the correlation coefficient |
After collecting data, how can we tell if there is a relationship between two variables? |
|
Estimating correlation and lines of best fit Comparing to the calculated results of linear regressions and the correlation coefficient |
How can we apply what we know about linear functions to statistics? |
|
Using linear models of data and interpret the slope and intercept of regression lines with various units |
How can correlation and linear regressions help us to understand the differences in men's and women's incomes? |
|
Using residual plots to analyze the strength of a linear model for data |
Should all bivariate data be modeled with a linear function? Are there other ways to tell if a linear model is appropriate besides a correlation coefficient? |
|
Using definitions and examples to explain understanding of correlation coefficients, residuals, and linear regressions |
What do correlations coefficients, linear regressions, and residuals really tell us about bivariate data? |
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