EngageNY
The Division of Polynomials
Build a true understanding of division of polynomials. Learners use their knowledge of multiplying polynomials to create an algorithm to divide polynomials. The area model of multiplication becomes the reverse tabular method of division.
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The Remainder Theorem
Time to put it all together! Building on the concepts learned in the previous lessons in this series, learners apply the Remainder Theorem to finding zeros of a polynomial function. They graph from a function and write a function from...
EngageNY
Graphing Systems of Equations
Expand on learners' understanding of quadratic-linear systems. Building on the graphic understanding developed in the previous lesson, pupils learn algebraic methods of solving the systems.
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Modeling a Context from Data (part 2)
Forgive me, I regress. Building upon previous modeling activities, the class examines models using the regression function on a graphing calculator. They use the modeling process to interpret the context and to make predictions...
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Multiplying Polynomials
There's only one way to multiply, right? Not when it comes to polynomials. Reach each individual by incorporating various representations to multiplying polynomials. This instructional activity approaches multiplying polynomials from all...
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Complex Number Division 1
Conjugating in the math classroom — and we're not talking verbs! The seventh lesson in a series of 32 introduces the class to the building blocks of complex number division. During the instruction, the class learns to find the...
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Representing Reflections with Transformations
In the 16th lesson in the series of 32 the class uses the concept of complex multiplication to build a transformation in order to reflect across a given line in the complex plane. The lesson breaks the process of reflecting across a line...
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Vectors and Stone Bridges
What does it take to build a stable arch? Pupils apply vectors and physics as they examine arched bridges and their structural integrity. They use vectors to represent the forces acting on the stone sections and make conclusions based on...
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Base Angles of Isosceles Triangles
Build confidence in proofs by proving a known property. Pupils explore two approaches to proving base angles of isosceles triangles are congruent: transformations and SAS. They then apply their understanding of the proof to more complex...
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Solving Problems in Two Ways—Rates and Algebra
Build confidence by using multiple approaches to problem solving! This resource uses a visual and algebraic approach to solving application problems. A discussion is included about efficient approaches to different problems.
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Recursive Challenge Problem—The Double and Add 5 Game
As a continuation of a previous activity, this activity builds on the concept of calculating the terms of a sequence. Pupils are challenged to determine the smallest starting term to reach a set number by a set number of rounds. Notation...
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The General Multiplication Rule
In the first installment of a 21-part module, scholars build on previous understandings of probability to develop the multiplication rule for independent and dependent events. They use the rule to solve contextual problems.
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Interpreting Rate of Change and Initial Value
Building on knowledge from the previous lesson, the second lesson in this unit teaches scholars to identify and interpret rate of change and initial value of a linear function in context. They investigate how slope expresses the...
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Magnitude
Build an understanding of the powers of 10. Pupils investigate the results of raising 10 to positive and negative powers. They relate this understanding to the magnitude these powers represent in this seventh lesson of 15.
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Increasing and Decreasing Functions 2
Explore linear and nonlinear models to help your class build their function skills. In a continuation of the previous lesson, learners continue to analyze and sketch functions that model real-world situations. They progress from linear...
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Nonlinear Models in a Data Context
How well does your garden grow? Model the growth of dahlias with nonlinear functions. In the instructional activity, scholars build on their understanding of mathematical models with nonlinear models. They look at dahlias growing in...
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Square Roots
Investigate the relationship between irrational roots and a number line with a resource that asks learners to put together a number line using radical intervals rather than integers. A great progression, they build on their understanding...
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Existence and Uniqueness of Square Roots and Cube Roots
Teach cube roots by building on an understanding of square roots. The third installment of a 25-part series asks learners to solve simple quadratic and cubic equations using roots. Scholars compare square roots and cube roots throughout...
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Comparing Irrational Numbers
Build on your classes' understanding of irrational numbers by comparing their values. The 13th lesson in the 25-part module has individuals estimate values of both perfect and non-perfect roots. They finish by graphing these numbers on a...
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Calculating Probabilities for Chance Experiments with Equally Likely Outcomes
Calculate theoretical probabilities and compare them to experimental probabilities. Pupils build on their knowledge of experimental probabilities to determine theoretical probabilities. Participants work several problems with the...
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Percent
Extend percent understandings to include percents less than one and greater than 100. A great lesson has pupils build upon their knowledge of percents from sixth grade. They convert between fractions, decimals, and percents that are less...
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Sampling Variability and the Effect of Sample Size
The 19th installment in a 25-part series builds upon the sampling from the previous unit and takes a larger sample. Pupils compare the dot plots of sample means using two different sample sizes to find which one has the better variability.
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Equivalent Ratios
Equivalent ratios show up on tape. Young mathematicians use tape diagrams to create equivalent ratios in the initial lesson on the topic. They learn the definition of equivalent ratios and use it to build others in the third segment of a...
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The Structure of Ratio Tables—Additive and Multiplicative
Build tables by understanding their structure. Scholars take a closer look at the structure of ratio tables in the 10th segment in a 29-part series. Individuals realize that the tables can be built using an additive or...
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