This problem allows the student to think geometrically about lines and then relate this geometry to linear functions. Or the student can work algebraically with equations in order to find the explicit equation of the line through two points (when that line is not vertical).
Material Type: Activity/Lab
This task requires students to use the normal distribution as a model for a data distribution. Students must use given means and standard deviations to approximate population percentages. There are several ways (tables, graphing calculators, or statistical software) that students might calculate the required normal percentages. Depending on the method used, answers might vary somewhat from those shown in the solution.
Material Type: Activity/Lab
This lesson is about properties of quadrilaterals and learning to investigate, formulate, conjecture, justify, and ultimately prove mathematical theorems. Students will: Analyze characteristics and properties of two- and three-dimensional geometric shapes; develop mathematical arguments about geometric relationships; and apply appropriate techniques, tools, and formulas to determine measurements.Explore relationships among classes of two- and three-dimensional geometric objects, make and test conjectures about them, and solve problems involving them. Employ forms of mathematical reasoning and proof appropriate to the solution of the problem at hand, including deductive and inductive reasoning, making and testing conjectures, and using counter examples and indirect proof. Identify, formulate and confirm conjectures. Establish the validity of geometric conjectures using deduction, prove theorems, and critique arguments made by others. (9th/10th Grade Math)
Material Type: Activity/Lab, Lecture, Lesson Plan, Teaching/Learning Strategy
This lesson focuses on students making decisions about what tools to apply to solve different problems related to quadratic expressions and equations. It is also intended to build awareness of the form an answer will take in order to help students make sense of the kind of problem they are solving. (9th/10th/11th Grade Math)
Material Type: Activity/Lab, Lecture, Lesson Plan, Teaching/Learning Strategy
This lesson unit is intended to help teachers assess how well students are able to visualize two-dimensional cross-sections of representations of three-dimensional objects. In particular, the lesson will help you identify and help students who have difficulties recognizing and drawing two-dimensional cross-sections at different points along a plane of a representation of a three-dimensional object.
Material Type: Assessment, Lesson Plan
This lesson unit is intended to help teachers assess how well students are able to: work with concepts of congruency and similarity, including identifying corresponding sides and corresponding angles within and between triangles; Identify and understand the significance of a counter-example; Prove, and evaluate proofs in a geometric context.
Material Type: Assessment, Lesson Plan
This lesson unit is intended to help you assess how well students are able to use geometric properties to solve problems. In particular, it will support you in identifying and helping students who have the following difficulties: Solving problems relating to using the measures of the interior angles of polygons; and solving problems relating to using the measures of the exterior angles of polygons.
Material Type: Assessment, Lesson Plan
This lesson unit is intended to help teahcers assess how well students solve problems involving measurement, and in particular, to identify and help students who have the following difficulties; computing measurements using formulas; decomposing compound shapes into simpler ones; using right triangles and their properties to solve real-world problems.
Material Type: Assessment, Lesson Plan
This lesson unit is intended to help teachers assess how well students are able to interpret exponential and linear functions and in particular to identify and help students who have the following difficulties: translating between descriptive, algebraic and tabular data, and graphical representation of the functions; recognizing how, and why, a quantity changes per unit intervale; and to achieve these goals students work on simple and compound interest problems.
Material Type: Assessment, Lesson Plan
This lesson unit is intended to help teachers assess how well students are able to use linear inequalities to create a set of solutions. In particular, the lesson will help teachers identify and assist students who have difficulties in: representing a constraint by shading the correct side of the inequality line; and understanding how combining inequalities affects a solution space.
Material Type: Assessment, Lesson Plan
This assessment task can be used with a single student or a small group of students. Each student needs his or her own set of numeral cards.
Material Type: Activity/Lab
These 3 word problems require students to solve addition and subtraction problems.
Material Type: Activity/Lab
The purpose of this task is for students to find different pairs of numbers that sum to 4.
Material Type: Activity/Lab
The purpose of this task is to help students understand the connection between counting and cardinality. Thus, oral counting and recording the number in digit form are the most important aspects of this activity. However, teachers can extend this by making a bar graph about how many students are wearing the color each day.
Material Type: Activity/Lab
Students work to understand the language of word problems, using specific words as clues to the mathematical operations embedded in the problem. Teacher will use examples of student work to uncover misconceptions and errors and help support the students in developing the ability to critically evaluate their own strategies.Mathematics tasks include: Ability to read a problem in context and choose an operation to solve the problem; Ability to set up a number sentence that represents the problem; Accurately and efficiently solves two-digit addition and subtraction equations; Understands how to compose and decompose numbers; Can prove a sum or difference is correct using pictures, words, and/or symbols. (2nd Grade Math)
Material Type: Activity/Lab, Lecture, Lesson Plan, Teaching/Learning Strategy
This lesson unit is intended to help teachers assess how well students: are able to use frequency graphs to identify a range of measures and make sense of this data in a real-world context; and understand that a large number of data points allow a frequency graph to be approximated by a continuous distribution.
Material Type: Assessment, Lesson Plan
This lesson unit is intended to help teachers assess how well students are able to interpret data using frequency graphs and box plots. In particular this unit aims to identify and help students who have difficulty figuring out the data points and spread of data from frequency graphs and box plots. It is advisable to use the lesson: Representing Data 1: Frequency Graphs, before this one.
Material Type: Assessment, Lesson Plan
This module fosters a careful understanding of the Common Core State Standards math shifts. Participants take a deep dive into the major work of grades K-8, build a deeper understanding of the coherence of the Standards, and work through sample problems that reflect the "rigor" expected by the Standards.
Material Type: Teaching/Learning Strategy, Unit of Study
This module provides participants with an introduction to the key shifts required by the Common Core State Standards for Math. Depending on the activities selected, this module could support up to four hours of Math PD.
Material Type: Teaching/Learning Strategy, Unit of Study
This presents a general discussion of the development of the Common Core Mathematics Standards and the aspirations within them for student college-and-career readiness and success.
Material Type: Teaching/Learning Strategy
