Author: genzlingec

8.F – Just A Little Salt Can Go A Long Way

genzlingec Assessment of CCSS-Math, Common Core State Standards Mathematics, ML Functions, ML Modeling, Technology Teaching Issues

Vernier_EasyTemp_large

There is no doubt that our society is advancing so much in the realm of technology.  It is our job as educators to integrate technology into our curriculum to prepare our students to be proficient and prepared for the future and able to understand technology when they are in their own careers.  It has also been a goal in the field of education to get students to learn how different subjects can be relatable to mathematics.  In this lesson, students must go beyond the task of computing numbers and creating a table of data to understanding the science behind why salt when added to water increases the overall time it takes for it to freeze or if it will freeze at all.  This may be a simple mathematics lesson, but it is an accurate example of what type of situations students will have to learn and understand if they are ever in the field of geology and understanding how elements of nature affects certain things.

Saltwater Vernier Probes Lesson

8.EE.B / 8.F.A. / HSA-CED.A Time to Sell Some Cars

genzlingec Algebra Teaching Issues, Assessment of CCSS-Math, Common Core State Standards Mathematics, Middle School Issues, ML Expressions & Equations, ML Functions, ML Modeling

With this problem, students are able to see an example of a real-world situation and understand how to answer a question about two different scenarios and see how they relate to one another.  It is important that students can see and understand that anything in the world can be related or traced back to math.  This is just one example.

Students in this lesson will have to understand proportional relationships between two linear equations then be able to create those equations from what they already know about what the equation for a line even looks like.  Students will be asked to graph their solutions in a table in order to see the comparisons of the two different car salesman and understand that even though an initial amount may be more than another, over a period of time the rate of change is more important to see who will make more at the end of the year.

Illustrative Mathematics Problem

G.SRT-Mathematical Proportions/Similarities in Real Life

genzlingec Common Core State Standards Mathematics, HS Geometry, HS Modeling, Picture Problems

 

Common Core State Standard

CCSS.MATH.CONTENT.HSG.SRT.A.2

Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

In order to find the height of the palm tree, a person must create a similar triangle triangle in relation to the tree itself.  A person must look at the top of a  tree and line it up to the sun.  Once this has been established, a person must measure the length of the trees shadow, their own shadow, and the height of the person.  The picture below is an example of how to create similar triangles.

Similar Triangles for Height

6.EE-Using Algebra Touch to Simplify Algebraic Expressions & Equations Using Distributive Property

genzlingec Algebra Teaching Issues, CCSS-Math Learning Progressions, Middle School Issues, ML Expressions & Equations, Technology Teaching Issues

The Algebra Touch app gives students the opportunity to physically move numbers and variables around an iPad screen to better understand how to simplify algebraic expressions.  Students who are trying to solve algebraic expressions on paper out of a textbook have a hard time seeing what needs to be done first and the steps to simplify.  With this app, students get walked through the procedures and have visual aids to help them understand what is really going on mathematically.

In this lesson, students will learn how to solve different algebraic equations and simplify expressions with an emphasis on the distribution property.  Students are already knowledgeable of how to simplify algebraic equations and expressions by addition, subtraction, multiplication, and division.  Algebra Touch allows students to visualize the reason why the distributive property works.  Teachers can explain the distributive property with some examples on the whiteboard, but once the students get the opportunity to manipulate the different parts of expressions themselves on the iPad, it will deepen their understanding.

Algebra Touch Lesson Plan

Algebra Expressions and Equations Worksheet

(Video showing steps on how to distribute and factoring out using Algebra Touch)