INVESTIGATING MATH

A BALANCING ACT

LEARNING TARGET: Students will be able to understand the concept of solving equations as a process of reasoning, and to be able to explain the reasoning process using properties of numbers.

STANDARDS:

• Primary: A-REI.A.1
• Similar to Regents Exam Questions A.REI.A.1: Identifying Properties 1a

BURIED TREASURE

LEARNING TARGET: To reinforce students’ previous learnings on graphing linear equations and to provide an opportunity to apply the skill to solve systems of equations using graphing.

STANDARDS:

• Primary: A.REI.10
• Secondary: A.REI.12
• Similar to Algebra I Common Core Exam: January 28, 2016 (Q#21)

COMPLETING THE SQUARE

LEARNING TARGET: Students explore the reasoning behind the procedure for completing the square given the expression x² + bx + _____.

The process of “completing the square” is the key idea in deriving the quadratic formula from a general quadratic: ax² + bx + c.

STANDARDS:

• Primary: A-REI.4
• Similar to Algebra I Common Core Exam: June 3, 2014 (Q#8); August 13, 2014 (Q#32)

EBOLA OUTBREAK

LEARNING TARGET: Students will be able to distinguish between exponential growth and linear growth. In particular: (A) exponential growth occurs when successive function values over the same interval are related multiplicatively; and (B) linear growth occurs when successive function values over the same interval are related additively (over a unit interval, this additive constant is the slope of the line).

STANDARDS:

• Primary: F-LE.1
• Secondary: F-LE.3
• Similar to Regents Exam Algebra I (Common Core): June 3, 2014 (Q#6); August 13, 2014 (Q#10)

FRUIT BASKET POLYNOMIALS

LEARNING TARGET: Students will learn how to add polynomials by developing an understanding that terms must be alike to add them. Students will be able to apply the concepts in adding polynomials to subtracting polynomials.

STANDARDS:

• Primary: A-APR.1

ALL THE NEWS THAT FITS

LEARNING TARGET: Students will be able to use key vocabulary in a word problem and solve equations to interpret linear functions.

STANDARDS:

• Primary: F-IF.4, F-IF.5, F-IF.6

GARDEN WALKWAY & MULTIPLYING POLYNOMIALS

LEARNING TARGET: Students will be able to use a picture to create a model in which various aspects of this picture are represented algebraically as expressions/equations in one variable. The three gardens represent a succession of what is known and not known. This Activity also requires students to reason about conservation of area, an important mathematical idea.

STANDARDS:

• Primary: A-CED.1
• Secondary: F-IF.2, F-BF.1a
• Similar to Regents Exam Algebra I (Common Core): June 3, 2014 (Q#34); August 13, 2014 (Q#36)

HIV & FUNCTIONS

LEARNING TARGET: Students will be able to understand how to use functions and how to represent a function algebraically. In this activity students are discovering how functions are an extension of the concepts of input and output that they learned in elementary mathematics. They build the understanding that functions show a cause-and-effect relationship between variables, where the value of the dependent variable is affected by the independent variable.

STANDARDS:

• Primary: F-IF.1, F-IF.2, F-IF.3

PICTURE FRAME

LEARNING TARGET: Students will be able to identify useful information that would help them solve an area problem and coordinate measurements in a picture with algebraic representations of quantities that can be derived from these measurements (i.e., lengths, widths, and areas). This activity relies heavily on an area model of multiplication and the principle of area conservation.

STANDARDS:

• Primary: A-CED.1
• Secondary: F-IF.2, F-BF.1A
• Similar to Algebra I Common Core Exam: June 3, 2014 (Q#34); August 13, 2014 (Q#36)

PRODUCT X

LEARNING TARGET: Students will expand their knowledge of operations with polynomials. Previously, students have added and subtracted polynomials. In this activity they will use visuals to multiply polynomials. Students will focus specifically on multiplying two binomials in this investigation.

STANDARDS:

• Primary: A-APR.1
• Similar to Regents Exam Questions A.APR.A.1: Operations with Polynomials (Q#1 - 5)

QUADRATIC EQUATIONS

LEARNING TARGET: Students will be able to identify the values of various components of quadratic equations by using a representation of throwing a ball into the air. Students will also discover how the parts of the equation relate to the graph of the equation.

STANDARDS:

• Primary: A-CED.1, A-CED.2

GRAPHING LINEAR EQUATIONS

LEARNING TARGET: Students will be able to graph a linear equation from the key information in a word problem. In this activity students are discovering how the y-intercept and slope relate to the starting number, and the relationship between the independent and dependent variables. However, teachers are not yet introducing these terms. Students are developing an idea of how to identify these values in a word problem and use that to create a linear graph.

STANDARDS:

• Primary: A-REI.11

ROAD TRIP

LEARNING TARGET: Students will explore translating real-world situations into algebraic equations and inequalities by using key terms and identifying the mathematical operations they represent. In this Activity, algebraic equations and inequalities are used to show students’ ability to compare the value of two quantities. Creating algebraic equations and inequalities is a key mathematical idea that can be leveraged when solving equations and inequalities.

STANDARDS:

• Primary: A-CED.1
• Secondary: A-REI.3, N-Q.1

A ROOM FULL OF GOLD

LEARNING TARGET: Students will explore unit conversions while they reason about situations in which it is appropriate to use multiplication and division. In this Activity, multiplication is used as a way of expressing the total amount of some quantity that is composed of a number of objects that each have this quantity. Division is used as a way of expressing the number of objects that fit into a space.

STANDARDS:

• Primary: N-Q.1
• Secondary: N-Q.2

SAVINGS ACCOUNT

LEARNING TARGET: Students will be able to solve systems of equations graphically. Students use key terms to create equations from a word problem that models a real world situation. Using these equations, they create two linear graphs and use the point of intersection on the graphs to form interpretations and make concrete statements in terms of what that point represents in the word problem.

STANDARDS:

• Primary: A.REI.C.6

SHOE SIZE & LINEAR FUNCTIONS

LEARNING TARGET: Students will be able to identify linear equations from real-world situations. In this activity, students develop a linear equation and use that equation to make predictions around the relationship between foot length and shoe size.

STANDARDS:

• Primary: F.LE.A.1.b

THE 'X' FACTOR

LEARNING TARGET: Students use visualizing to factor trinomials, specifically factoring trinomials into two binomials. Students understand that factoring trinomials is a process used to find the two binomials, that when multiplied equal the original trinomial.

STANDARDS:

• Primary: A.SSE.A.2
• Secondary: A.SSE.1 (a,b)
• Similar to Algebra I Common Core Exam: June 17, 2015 (Q#3); January 26, 2015 (Q#3)

WHAT'S MY PAY RATE?

LEARNING TARGET: Students will understand the concept of solving equations without necessarily solving them algebraically. This activity is fostering a conceptual understanding of solving equations through the process of balancing equations.

STANDARDS:

• Primary: A-REI.A.3
• Secondary: A-REI.A.1
• Similar to Algebra I Common Core Exam: August 17, 2016 (Q#14)

POLICE SHOOTINGS CREATE EQUATIONS

LEARNING TARGET: Students use a real-world situation to learn how to create equations that represent situations. Students are using their ability to gather key information and create visual representations to assist them in creating the equation.

STANDARDS:

• Primary: A-CED.1, A-CED.2

SUMMING CONSECUTIVE ODD NUMBERS

LEARNING TARGET: Students explore algebraic patterns using geometric figures, and generate and prove a conjecture. The conjecture is that 1+3+5+7+... +(2n-1) = n² is valid. A secondary goal is to deepen students’ understanding of the area model of multiplication through focusing on structural aspects of how the area of perfect squares increases as the length of the sides of the square increases incrementally by 1.

STANDARDS:

• Primary: A-SSE.2
• Secondary: A-SSE.3, A-CED.1
• Similar to Algebra I Common Core Exam: June 3, 2014 (Q#9)