Mrs. Villamar - Math

I was the original and founding 7th grade Math teacher here at Sonoran Foothills when the school opened in 2016. It is my 17th year teaching 7th grade Mathematics! It's so much fun to work with the siblings and cousins of former students and stay in touch with the amazing families I have met throughout the years. I love teaching Math and seeing the "Ah-ha" moments in class when students make connections and truly understand. I am here to help you be successful in Math this year. My goal is for you to be challenged at the appropriate level, and gain more confidence and understanding in your mathematical skills. 

I grew up in Cleveland, Ohio and moved to Phoenix, AZ to attend Arizona State University. In 2006, I graduated with my bachelors degree in K-8 Elementary Education, with a Mathematics Specialist emphasis. I am also highly qualified in middle school Mathematics and working towards my gifted endorsement.

My husband and I have 3 children. Lilyanah is 8 years old, and Rafael is 5 years old and Jax is 3 years old. We love going to the park, playing soccer, walking, bike riding and spending time with our extended family.

I also privately tutor high school Math students throughout the week after school. It's neat to see how much 7th grade Math concepts connect to upper grade Math!

The 4 major areas in 7th Grade Math  include:

1.) Proportional Reasoning: -Develop an understanding of proportional relationships -Solve problems involving tax, tip, discount, percent increase and decrease -Apply proportional reasoning to solve problems including scale drawings 2.) Number Sense:  -Interpret and explain rules for adding, subtracting, multiplying, and dividing positive and negative numbers. -Simplify expressions -Solve equations -Understand that decimals, fractions and percents are different representations of rational numbers 3.) Geometry: -Finding the area and circumference of a circle -Calculating surface area of 3D objects -Solve real world problems involving area and volume 4.) Statistics -Compare two data distributions -Begin work with random sampling For a specific outline of the 7th grade common core state standards, go to this website: Math Final Seventh Grade Standards 12_9_2016.pdf (azed.gov)

Unit 1 Overview and Explanation

Link to Family Materials: https://im.openupresources.org/7/families/index.html

Unit 1: Scale Drawings

"Work with scale drawings in grade 7 draws on earlier work with geometry and geometric measurement. Students began to learn about two- and three-dimensional shapes in kindergarten, and continued this work in grades 1 and 2, composing, decomposing, and identifying shapes. Students’ work with geometric measurement began with length and continued with area. Students learned to “structure two-dimensional space,” that is, to see a rectangle with whole-number side lengths as an array of unit squares, or rows or columns of unit squares. In grade 3, students distinguished between perimeter and area. They connected rectangle area with multiplication, understanding why (for whole-number side lengths) multiplying the side lengths of a rectangle yields the number of unit squares that tile the rectangle. They used area diagrams to represent instances of the distributive property. In grade 4, students applied area and perimeter formulas for rectangles to solve real-world and mathematical problems, and learned to use protractors. In grade 5, students extended the formula for the area of a rectangle to include rectangles with fractional side lengths. In grade 6, students built on their knowledge of geometry and geometric measurement to produce formulas for the areas of parallelograms and triangles, using these formulas to find surface areas of polyhedra.

In this unit, students study scaled copies of pictures and plane figures, then apply what they have learned to scale drawings, e.g., maps and floor plans. This provides geometric preparation for grade 7 work on proportional relationships as well as grade 8 work on dilations and similarity.

Students begin by looking at copies of a picture, some of which are to scale, and some of which are not. They use their own words to describe what differentiates scaled and non-scaled copies of a picture. As the unit progresses, students learn that all lengths in a scaled copy are multiplied by a scale factor and all angles stay the same. They draw scaled copies of figures. They learn that if the scale factor is greater than 1, the copy will be larger, and if the scale factor is less than 1, the copy will be smaller. They study how area changes in scaled copies of an image.

Next, students study scale drawings. They see that the principles and strategies that they used to reason about scaled copies of figures can be used with scale drawings. They interpret and draw maps and floor plans. They work with scales that involve units (e.g., “1 cm represents 10 km”), and scales that do not include units (e.g., “the scale is 1 to 100”). They learn to express scales with units as scales without units, and vice versa. They understand that actual lengths are products of a scale factor and corresponding lengths in the scale drawing, thus lengths in the drawing are the product of the actual lengths and the reciprocal of that scale factor. They study the relationship between regions and lengths in scale drawings. Throughout the unit, they discuss their mathematical ideas and respond to the ideas of others (MP3, MP6). In the culminating lesson of this unit, students make a floor plan of their classroom or some other room or space at their school. This is an opportunity for them to apply what they have learned in the unit to everyday life (MP4).

In the unit, several lesson plans suggest that each student have access to a geometry toolkit. Each toolkit contains tracing paper, graph paper, colored pencils, scissors, centimeter ruler, protractor (clear protractors with no holes that show radial lines are recommended), and an index card to use as a straightedge or to mark right angles. Providing students with these toolkits gives opportunities for students to develop abilities to select appropriate tools and use them strategically to solve problems (MP5). Note that even students in a digitally enhanced classroom should have access to such tools; apps and simulations should be considered additions to their toolkits, not replacements for physical tools.

Note that the study of scaled copies is limited to pairs of figures that have the same rotation and mirror orientation (i.e. that are not rotations or reflections of each other), because the unit focuses on scaling, scale factors, and scale drawings. In grade 8, students will extend their knowledge of scaled copies when they study translations, rotations, reflections, and dilations."

 

*https://im.openupresources.org/7/teachers/teacher_course_guide.html#unit1scale-drawings

Unit 2: Introducing Proportional Relationships

Interactive Resources/Websites/Games to help your child:

1.) Khan Academy for Illustrative Mathematics Unit 2 provides videos, interactive practice, quizzes and even an end of the unit test! Get instant help that directly correlates to each section of Unit 2 in your binder.

Use Google Chrome or Safari:
Click Here: https://www.khanacademy.org/math/illustrative-math/7th-grade-illustrative-math

2.) Practice matching equivlent ratios! This will help you identify if the given table shows a proportional relationship- if all the ratios are equal!
Click Here: http://www.sheppardsoftware.com/mathgames/ratios/MatchingEqualRatios.htm

3.) Matching Ratios with Unit Rates

Click Here: http://www.sheppardsoftware.com/mathgames/ratios/MatchingRates.htm

4.) Ratios, Rates, and Proportions JEOPARDY GAME!

Click Here: https://jeopardylabs.com/play/ratios-unit-rate-and-proportions

Family Materials from Illustrative Mathematics

Unit 2: Introducing Proportional Relationships

The following is taken straight from the open resources family materials page website! You can view the charts/graphs as well by clicking this link:

https://im.openupresources.org/7/teachers/2/family_materials.html

Representing Proportional Relationships with Tables

This week your student will learn about proportional relationships. This builds on the work they did with equivalent ratios in grade 6. For example, a recipe says “for every 5 cups of grape juice, mix in 2 cups of peach juice.” We can make different-sized batches of this recipe that will taste the same.

The amounts of grape juice and peach juice in each of these batches form equivalent ratios.

The relationship between the quantities of grape juice and peach juice is a proportional relationship. In a table of a proportional relationship, there is always some number that you can multiply by the number in the first column to get the number in the second column for any row. This number is called the constant of proportionality.

In the fruit juice example, the constant of proportionality is 0.4. There are 0.4 cups of peach juice per cup of grape juice.

Here is a task you can try with your student:

Using the recipe “for every 5 cups of grape juice, mix in 2 cups of peach juice”

Solution:

Representing Proportional Relationships with Equations

This week your student will learn to write equations that represent proportional relationships. For example, if each square foot of carpet costs $1.50, then the cost of the carpet is proportional to the number of square feet.

The constant of proportionality in this situation is 1.5. We can multiply by the constant of proportionality to find the cost of a specific number of square feet of carpet.

We can represent this relationship with the equation c=1.5f  , where f  represents the number of square feet, and c  represents the cost in dollars. Remember that the cost of carpeting is always the number of square feet of carpeting times 1.5 dollars per square foot. This equation is just stating that relationship with symbols.

The equation for any proportional relationship looks like y=kx  , where x  and y  represent the related quantities and k  is the constant of proportionality. Some other examples are y=4x  and d=13 t  . Examples of equations that do not represent proportional relationships are y=4+x  , A=6s 2   , and w=36L   .

Here is a task to try with your student:

Solution:

Representing Proportional Relationships with Graphs

This week your student will work with graphs that represent proportional relationships. For example, here is a graph that represents a relationship between the amount of square feet of carpet purchased and the cost in dollars.

Each square foot of carpet costs $1.50. The point (10,15)  on the graph tells us that 10 square feet of carpet cost $15.

Notice that the points on the graph are arranged in a straight line. If you buy 0 square feet of carpet, it would cost $0. Graphs of proportional relationships are always parts of straight lines including the point (0,0)  .

Here is a task to try with your student:

Create a graph that represents the relationship between the amounts of grape juice and peach juice in different-sized batches of fruit juice using the recipe “for every 5 cups of grape juice, mix in 2 cups of peach juice.”

Solution:

1. How much peach juice would you mix with 20 cups of grape juice?
2. How much grape juice would you mix with 20 cups of peach juice?
3. 8 cups of peach juice. Sample reasoning: We can multiply any amount of grape juice by 0.4 to find the corresponding amount of peach juice, 20⋅ (0.4)=8  .
4. 50 cups of grape juice. Sample reasoning: We can divide any amount of peach juice by 0.4 to find the corresponding amount of grape juice, 20÷0.4=50  .
5. Write an equation that represents that relationship between the amounts of grape juice and peach juice in the recipe “for every 5 cups of grape juice, mix in 2 cups of peach juice.”
6. Select all the equations that could represent a proportional relationship:
   1. K=C+273 
   2. s=14 p 
   3. V=s 3  
   4. h=14−x 
   5. c=6.28r 
7. Answers vary. Sample response: If p  represents the number of cups of peach juice and g  represents the number of cups of grape juice, the relationship could be written as p=0.4g  . Some other equivalent equations are p=25 g  , g=52 p  , or g=2.5p  .
8. B and E. For the equation s=14 p  , the constant of proportionality is 14   . For the equation c=6.28r  , the constant of proportionality is 6.28.