This task asks students to use inverse operations to solve the equations …
This task asks students to use inverse operations to solve the equations for the unknown variable, or for the designated variable if there is more than one. Two of the equations are of physical significance and are examples of Ohm's Law and Newton's Law of Universal Gravitation.
This lesson unit is intended to help teachers assess how well students …
This lesson unit is intended to help teachers assess how well students are able to: use the Pythagorean theorem to derive the equation of a circle; and translate between the geometric features of circles and their equations.
This lesson unit is intended to help teachers assess how well students …
This lesson unit is intended to help teachers assess how well students are able to: translate between the equations of circles and their geometric features; and sketch a circle from its equation.
This task requires students to use the fact that on the graph …
This task requires students to use the fact that on the graph of the linear equation y=ax+c, the y-coordinate increases by a when x increases by one. Specific values for c and d were left out intentionally to encourage students to use the above fact as opposed to computing the point of intersection, (p,q), and then computing respective function values to answer the question.
Lesson focuses on creating equivalent expressions. Isolating the variable. Focus Questions: What …
Lesson focuses on creating equivalent expressions. Isolating the variable. Focus Questions: What value of the variable will create two equivalent expressions? How can this solution be checked?How can inverse operations be used to isolate the variable?What operation(s) will be needed to isolate the variable? Lesson Segment 1: Accessing Background knowledge, Launch-Finding Equivalent Expressions. Lesson segment 2: What value of the variable will create two equivalent expressions? How can this solution be checked? Lesson Segment 3: How can inverse operations be used to isolate the variable? Lesson Segment 4: Summarize Assessment Plan:observation, questioning, performance
In this problem students must transform expressions using the distributive, commutative and …
In this problem students must transform expressions using the distributive, commutative and associative properties to decide which expressions are equivalent.
This is a standard problem phrased in a non-standard way. Rather than …
This is a standard problem phrased in a non-standard way. Rather than asking students to perform an operation, expanding, it expects them to choose the operation for themselves in response to a question about structure. The problem aligns with A-SSE.2 because it requires students to see the factored form as a product of sums, to which the distributive law can be applied.
The purpose of this task is to directly address a common misconception …
The purpose of this task is to directly address a common misconception held by many students who are learning to solve equations. Because a frequent strategy for solving an equation with fractions is to multiply both sides by a common denominator (so all the coefficients are integers), students often forget why this is an "allowable" move in an equation and try to apply the same strategy when they see an expression.
Visually represent two unique fractions that are equivalent to a given fraction. …
Visually represent two unique fractions that are equivalent to a given fraction. The fractional value is shown on a number line after you check to see if your fraction is correct. Equivalent Fraction Finder is one of the Interactivate assessment explorers.
In this interactive activity a user identifies two pairs of equivalent fractions …
In this interactive activity a user identifies two pairs of equivalent fractions for a given random fraction or one of the player's own and the user creates their representations by dividing and shading either a square or circular region. The fractions are shown as locations on the number line and their equivalency is demonstrated when they are at the same point. The user has the ability to construct a table of equivalent fractions. Instructions and exploration questions are given.
Visually represent two unique fractions that are equivalent to a given fraction. …
Visually represent two unique fractions that are equivalent to a given fraction. The fractional value is shown on a number line as you color in the fraction. Equivalent Fraction Pointer is one of the Interactivate assessment explorers.
This activity is used in my classroom for intervention when students have …
This activity is used in my classroom for intervention when students have a struggle with Fractional Understanding and Equivalence and then struggle with Ratios and Unit Rates in seventh grade RP.
The purpose of the task is to get students to reflect on …
The purpose of the task is to get students to reflect on the definition of decimals as fractions (or sums of fractions), at a time when they are seeing them primarily as an extension of the base-ten number system and may have lost contact with the basic fraction meaning. Students also have their understanding of equivalent fractions and factors reinforced.
The accuracy and simplicity of this experiment are amazing. A wonderful project …
The accuracy and simplicity of this experiment are amazing. A wonderful project for students, which would necessarily involve team work with a different school and most likely a school in a different state or region of the country, would be to try to repeat Eratosthenes' experiment.
An introduction to the iterative decoding revolution. Learn about the experimental approach …
An introduction to the iterative decoding revolution. Learn about the experimental approach to error-correcting codes that has changed electronic communications. Topics include Turbo Codes, Low-Density Parity-Check Codes, and serially concatenated codes. Final projects involve the design of an error-correcting code, experiments to predict its performance, and the written and oral presentation of the results. Programming experience and a course in probability are required. Instruction and practice in oral and written communication provided. This course introduces students to iterative decoding algorithms and the codes to which they are applied, including Turbo Codes, Low-Density Parity-Check Codes, and Serially-Concatenated Codes. The course will begin with an introduction to the fundamental problems of Coding Theory and their mathematical formulations. This will be followed by a study of Belief Propagation--the probabilistic heuristic which underlies iterative decoding algorithms. Belief Propagation will then be applied to the decoding of Turbo, LDPC, and Serially-Concatenated codes. The technical portion of the course will conclude with a study of tools for explaining and predicting the behavior of iterative decoding algorithms, including EXIT charts and Density Evolution.
In this math activity, learners are presented with a problem: two bowls …
In this math activity, learners are presented with a problem: two bowls are suspended from the ceiling by springs. One bowl is lower than the other. In one bowl, you can only place marbles; in the other bowl, you can only place bingo chips. Learners investigate how many items must be placed in each bowl so that the heights of the bowls are the same, and in doing so, solve a system of linear equations. This lesson guide includes questions for learners, assessment options, extensions, and reflection questions.
Students learn that buoyancy is responsible for making boats, hot air balloons …
Students learn that buoyancy is responsible for making boats, hot air balloons and weather balloons float. They calculate whether or not a boat or balloon will float, and calculate the volume needed to make a balloon or boat of a certain mass float. Conduct the first day of the associated activity before conducting this lesson.
This lesson unit is intended to help you assess how well students …
This lesson unit is intended to help you assess how well students are able to: solve simple problems involving ratio and direct proportion; choose an appropriate sampling method; and collect discrete data and record them using a frequency table.
In this activity, students will estimate the height of our Commons (flagpole, …
In this activity, students will estimate the height of our Commons (flagpole, building, etc) using multiple methods.
Note: My students used homemade clinometers (protractor, string, weight). In the past, when students used a clinometer app we did not get as accurate results.
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