AB
... with solutions from Texas Instruments. The TI in Focus program supports teachers in preparing students for the AP® Calculus AB and BC test. Our library of files covers free-response questions (FRQ) from past exams through the lens of graphing technology. Below you’ll find released AP® Calculus ...https://education.ti.com/en/resources/ap-calculus/taylor-polynomials-power-series
AP® Calculus | BC6 2019 Module | Texas Instruments
...his problem asks for terms of Taylor polynomials and Maclaurin series of several functions, as well as approximations using them. Go to resource library BC6 Planning and Resources Objectives Students understand that the product of a whole number n and a fraction (a/b) is (na/b). Vocabul...https://education.ti.com/en/resources/ap-calculus/taylor-polynomials-power-series/sequence3/2019-bc6
AP® Calculus | BC2 2020 Module | Texas Instruments
... Method is one approximation technique used, and the tabular values are also used in creating a Taylor polynomial approximation. Go to resource library BC2 Planning and Resources Objectives Students should understand that when adding fractions, the fractions are marked off end to end on a...https://education.ti.com/en/resources/ap-calculus/taylor-polynomials-power-series/sequence4/2020-bc2
Ratios & Proportions
Ratios & Proportions website This lesson helps students to understand that ratios associate two or more quantities that vary together. 393695 What is a Ratio? Planning and Resources ...https://education.ti.com/en/building-concepts/activities/ratios
Extending Exponents
...notation, and interpret and explain numerical expressions involving exponents that are 0, negative, or \(\frac{1}{2}\) or \(\frac{1}{3}\). Vocabulary exponent base factor cube square power In this lesson students investigate how patterns in the computations for \(a^n, (ab)^n, (a^...https://education.ti.com/en/building-concepts/activities/expressions/sequence1/extending-exponents
Building a Table of Ratios
... strategies for finding equivalent ratios in a table. They understad the role of multiplication and addition in generating equivalent ratios. Vocabulary ratio equivalent ratio Students generate equivalent ratios in a table, where values in each row of the table are a multiple of the ...https://education.ti.com/en/building-concepts/activities/ratios/sequence1/building-a-table-of-ratios
Dividing a Fraction by a Fraction
...hey use the relationship between multiplication and division to explain that a division problem can be rewritten as a multiplication problem. Vocabulary identity element of multiplication This lesson can be used to develop an understanding of dividing a fraction (a/b) by the fraction ...https://education.ti.com/en/building-concepts/activities/fractions/sequence-1/dividing-a-fraction-by-a-fraction
Solving Equations
...rpret the solution in terms of the equation or context as well as recognize when one solution strategy might be more efficient than another Vocabulary linear equation solution identity In this lesson students draw upon tools learned in previous work and focus on making strategic c...https://education.ti.com/en/building-concepts/activities/expressions/sequence1/solving-equations
Building Expressions
...ddition. They use a variety of strategies, including rewriting an expression and properties of operations, to develop equivalent expressions. Vocabulary expression variable constant associative property commutative property distributive property equivalent expressions In this lesson ...https://education.ti.com/en/building-concepts/activities/expressions/sequence1/building-expressions
What's a Solution to a System of Equations?
...he solution in terms of the graphs of the two equations, and identify characteristics of equations that will lead to each possible outcome. Vocabulary system of linear equations in two variables intersection slope parallel lines solution to a system of two linear equations In this...https://education.ti.com/en/building-concepts/activities/expressions/sequence1/what-is-a-solution-to-a-system-of-equations
Visualizing Systems of Linear Equations
...ce in the mobile with moves that preserve algebraic solutions, and find solutions to systems of linear equations in more than one variable. Vocabulary equation system of linear equations in two variables In this lesson students will reason about solutions to systems of equations w...https://education.ti.com/en/building-concepts/activities/expressions/sequence1/visualizing-systems-of-linear-equations
Moving from Proportional Relationships to Linear Equations
...ph using similar triangles, and connect the equation for a proportional relationship, \(y = mx\), to the equation for a line, \(y = mx+b\). Vocabulary proportional relationship linear equation intercept In this lesson students use previous experience with proportional relationship...https://education.ti.com/en/building-concepts/activities/expressions/sequence1/proportional-relationships-to-linear-equations
Adding Fractions with Unlike Denominators
...n be added by creating equivalent fractions that have the same denominator, then use the process for adding fractions with like denominators. Vocabulary congruent common factor This lesson uses unit squares to help students investigate addition and subtraction of fractions with unlik...https://education.ti.com/en/building-concepts/activities/fractions/sequence-1/adding-fractions-with-unlike-denominators
Units Other Than a Unit Square
...compared if they refer to the same whole. They also recognize that fractions can only be added or subtracted if they refer to the same whole. Vocabulary unit fraction equivalent fraction This lesson helps students to understand the importance of the unit by approaching fractions usin...https://education.ti.com/en/building-concepts/activities/fractions/sequence-1/units-other-than-a-unit-square
Multiplying Fractions by a Whole Number
... Whole Number Planning and Resources Objectives Students understand that the product of a whole number n and a fraction (a/b) is (na/b). Vocabulary commutative property of multiplication This lesson can be used to develop multiplication of a fraction by a whole number. 393722 Mu...https://education.ti.com/en/building-concepts/activities/fractions/sequence-1/multiplying-fractions-by-a-whole-number
Mixed Numbers
...rator is less than the denominator and that an improper fraction is any fraction whose numerator is equal to or greater than the denominator. Vocabulary improper fraction proper fraction mixed number This lesson uses interactive number lines to help students investigate mixed numbers...https://education.ti.com/en/building-concepts/activities/fractions/sequence-1/mixed-numbers
Equations and Operations
...al moves related to equations and moves that do not preserve solutions. They can describe a strategy for finding a solution for an equation. Vocabulary expression equation variable solution In this lesson students investigate the relationship between the solution to an equation and ...https://education.ti.com/en/building-concepts/activities/expressions/sequence1/equations-and-operations
Solving Systems of Equations Algebraically
...uations in two variables, in particular the methods of elimination and substitution and determine elegant approaches to finding a solution. Vocabulary system of linear equations in two variables substitution solution to a system In this lesson students will investigate pathways fo...https://education.ti.com/en/building-concepts/activities/expressions/sequence1/solving-systems-of-equations-algebraically
Using Structure to Solve Equations
...__) = y or a + (__) = y as looking for a missing factor or addend respectively and use arithmetic order of operations to determine solutions. Vocabulary expression equation solution factor addend In this lesson students reason about the structure of expressions on either side of an e...https://education.ti.com/en/building-concepts/activities/expressions/sequence1/using-structure-to-solve-equations
Adding and Subtracting Fractions with Like Denominators
...their sum is represented by joining end to end the segment of length for one fraction to the segment of the length represented by the second. Vocabulary properties of addition This lesson uses interactive number lines to investigate addition and subtraction of fractions that refer to...https://education.ti.com/en/building-concepts/activities/fractions/sequence-1/adding-and-subtracting-fractions-with-like-denominators
What is a Fraction? - Texas Instruments
...number line. They use a number line to interpret the following: 1. (a/b) is a copies of (1/b) 2. (a*n/n) is a fraction 3. (0/n) is equal to 0 Vocabulary fraction numerator denominator unit fraction This lesson helps students understand and visualize a fraction as a number that can be ...https://education.ti.com/en/building-concepts/activities/fractions/sequence-1/what-is-a-fraction
Building Expressions in Two Variables
...ntify equivalent expressions involving rational numbers and explain why they are equivalent using properties of multiplication and addition Vocabulary expression equivalent expressions rational numbers integers distributive property of multiplication over addition In this lesson s...https://education.ti.com/en/building-concepts/activities/expressions/sequence1/building-expressions-in-two-variables
Equivalent Fractions - Texas Instruments
... compare and express the relationships between two fractions using the symbols and justify the conclusions by using a visual fraction model. Vocabulary equivalent fractions improper fractions This lesson helps students understand that two fractions are equivalent (or equal) if they ...https://education.ti.com/en/building-concepts/activities/fractions/sequence-1/equivalent-fractions
Dividing a Fraction by a Whole Number
...rstand that dividing a unit fraction by a whole number partitions the unit fraction into the number of pieces determined by the whole number. Vocabulary non-unit fraction quotient This lesson uses a unit square to explore division of fractions by whole numbers. 393724 Dividing a Fract...https://education.ti.com/en/building-concepts/activities/fractions/sequence-1/dividing-a-fraction-by-a-whole-number
Dividing a Whole Number by a Fraction
...They recognize that dividing a whole number c by a fraction (a/b) means you have to find how many groups or partial groups of (a/b) are in c. Vocabulary perfect squares In this lesson, unit squares are used to investigate division of whole numbers by a fraction. 393725 Dividing a Whol...https://education.ti.com/en/building-concepts/activities/fractions/sequence-1/dividing-a-whole-number-by-a-fraction