MANIA
Summer School Math Curriculum:
Essential standards taught through real-life application
and examples/ with a specific focus on nutrition and
wellness
Day 1:
Introduction
Obje ctives:
-Students and teachers will get to know each other
-Students will learn and understand the rules and expectations
Activities:
-Icebreakers (examples listed do not need to be used but may act as guidelines for
icebreakers)
Getting to Know You Bingo
Students will receive a Bingo card but with a variation on the normal game. Instead of
numbers there are statements with a line following them that is big enough for a name.
Example statements are: Has an 8 letter name, was born in the 4th month of the year, has
<3 siblings, has read 2^3 books, owns one or more pets, speaks two languages, plays q
sport, etc… Each student must write down the name of the person who fits the descriptor.
Fizz Buzz
Everyone sits in a circle and one person starts the game by saying a number
anywhere from 1-99. Each player then counts the next number in turn. However, any
number that has the number 3 or is divisible by 3 is replaced by the word “fizz”. Students
must also replace any number that has or is divisible by 5 with the word “buzz”.
The game would go as follows: 1, 2, fizz, 4, buzz, fizz, 7, 8, fizz, buzz, 11, fizz, fizz, 14, fizz
buzz, etc…
A person is out if they do not follow the rules either once or you can have a 3-strike system.
-Classroom Rules/Expectations
-Pre-test
Day 2:
Population Estimate with Capture and Recapture
the Beans*1
Obje ctives:
Students will:
-be able to recognize equivalent ratios
-determine good and poor estimates
-solve proportions to estimate population size
-represent the population size in scientific notation.
Essential Questions:
What is the definition of a proportion?
What is the definition of a ratio?
What are the differences between the two?
When would using scientific notation be useful?
Activities:
This is an introduction into how scientists use random sampling to determine a population of
birds in a particular area. In pairs/small groups, students will mark, count and record samples
of white beans from a cup. (See activity sheet).
Students should write and solve a proportion representing each trial with the beans. Results
won't be perfect, but most answers should fall within a reasonable range of the actual
number of beans in the cup.
Students should take additional samples then determine what percent of their population
estimates fall within the interval they say is acceptable. By doing this, students have a frame
of reference to determine if an estimate is good or poor.
Students should be discouraged from counting the beans instead of using proportions
during the activity. However, once they've committed to an answer, they can count the
actual number of beans in the cup to know how reasonable their calculated estimate is.
Then students will take their estimates and use a scale factor to represent the actual
population as represented by the population of birds in North America.
1
adapted from illuminations.nctm.org
Standards:
8.EE: Expressions and Equations-Work with radicals and integer exponents.
8.EE.3: Use numbers expressed in the form of a single digit times and integer power of 10 to
estimate very large or very small quantities, and to express how many times as much one is
than the other. For example, estimate the population of the United States as 3x108and the
population of the world as 7x109, and determine that the world population is more than 20
times larger.
Day 3-4
From the Line*2
Obje ctives:
Students will be able to:
-determine the fraction of free-throws a basketball player has attempted and made
-interchange fraction of made free-throws (obtained on Day 3) into a percentage
-compare their percentages with other classmates to determine who has the best
percentage.
Essential Questions:
How can we determine which student has the best free-throw percentage?
What are the ways in which fractions can be converted to percents?
Do you think 20 shots are enough to determine who the best free-throw shooter is?
Describe your strategy for writing the equation to represent how many free throws (y) a
student would make if they shot (x) free throws.
Activities:
Day 3 :
Each student will shoot 20 free throws.
Students will collect data on made baskets out of attempted baskets.
Students will create a table to represent their missed vs. made shots out of 20 attempts.
Day 4 :
Each student will individually convert his or her fraction into a percent.
2
adapted from mathlicious.com
Students will discuss the different ways in which the obtained data can be represented in
graph form and in function form.
Standards:
7.RP: Ratios and Proportional Relationships-Analyze proportional relationships and use them
to solve real-world and mathematical problems.
7.RP.1: Compute unit rates associated with ratios of fractions, including ratios of lengths,
areas, and other quantities measured in like or different units. For example, if a person
walks ½ mile in each ¼ hour, compute the unit rate as the complex fraction ½/¼ miles per
hour, equivalently 2 miles per hour.
7.RP.2: Recognize and represent proportional relationships between quantities.
a.
Decide whether two quantities are in a proportional relationship, e.g., by testing for
equivalent ratios in a table, or graphing on a coordinate plane and observing whether the
graph is a straight line through the origin.
b.
Identify the constant of proportionality (unit rate) in tables, graphs, equations,
diagrams, and verbal descriptions of proportional relationships.
c.
Represent proportional relationships by equations. For example, if total cost t is
proportional to the number n of items purchased at a constant price p, the relationship
between the total cost and the number of items can be expressed as t = pn.
7.RP.3: Use proportional relationships to solve multi-step ratio and percent problems.
Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees,
percent increase and decrease, percent error.
8.F: Functions-Use functions to model relationships between quantities
8.F.4: Construct a function to model a linear relationship between two quantities. Determine
the rate of change and initial value of the function from a description of a relationship or from
two (x, y) values, including reading these from a table or from a graph. Interpret the rate of
change and initial value of a linear function in terms of the situation it models, and in terms
of its graph or a table of values.
Day 5
Continued from Day 3-4
Obje ctive:
Students will be able to create graphs that accurately represent their individual data of
made vs. attempted free-throws.
Essential Questions:
What information does the graph provide you that the raw data from the experiment did not?
Activities:
Each student will create a graph to represent their data.
Standards:
8.F: Functions-Use functions to model relationships between quantities
8.F.4: Construct a function to model a linear relationship between two quantities. Determine
the rate of change and initial value of the function from a description of a relationship or from
two (x, y) values, including reading these from a table or from a graph. Interpret the rate of
change and initial value of a linear function in terms of the situation it models, and in terms
of its graph or a table of values.
Day 6:
Order of Operations BINGO
Obje ctives:
Students will evaluate expressions by properly applying the order of operations.
Essential Question:
What are real-world situations in which you would have to apply the order of operations?
Activities:
Students will participate in order of operations BINGO (difficulty of problems will be
determined by pre-test results)
Standards:
6.EE: Expressions and Equations- Apply and extend previous understandings of arithmetic to
algebraic expressions.
6.EE.3: Apply the properties of operations to generate equivalent expressions. For example,
apply the distributive property to the expression 3 (2 + x) to produce the equivalent
expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce
the equivalent expression 6(4x + 3y); apply properties of operations to y + y + y to produce
the equivalent expression 3y.
Day 7:
Hi, BMI*3
Obje ctive:
-Use inequalities to determine weight status.
-Students will calculate BMI for various celebrities and determine their weight status:
underweight, healthy, overweight or obese.
Essential Questions:
Why is it important for a person to know their own BMI?
Baltimore Ravens linebacker Ray Lewis has a BMI of almost 33; do you think he is really
obese?
When America Ferrera (aka Ugly Betty) lost weight recently, how did her BMI change and
why?
Whose BMI do you think is greater: Harry Potter from the first movie or Harry Potter from the
most recent one?
How would the graph of an inequality apply to this situation better than a graph of a linear
relationship?
Activities:
Students will watch a quick clip from CBS news about obesity in America. Students will be
given the formula for calculating BMI (Body Mass Index l1 · 703ℎ2 ).
Students will use order of operations to determine the BMI of celebrities.
Provide students with a graph of an inequality that represents the comparison between
weight and height and the different categories for the BMI and have students determine if
the graph is linear or non linear.
Standards:
6.EE: Expressions and Equations- Apply and extend previous understandings of arithmetic to
algebraic expressions.
3
*adapted
from mathlicious.com
6.EE.2c: Write, read, and evaluate expressions in which letters stand for numbers. Evaluate
expressions at specific values of their variables. Include expressions that arise from
formulas used in real-world problems. Perform arithmetic operations, including those
involving whole-number exponents, in the conventional order when there are no
parentheses to specify a particular order (Order of Operations). For example, use the
formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of
length s = ½ .
6.EE: Expressions and Equations- Reason about and solve one-variable equations and
inequalities.
6.EE.5: Understand solving an equation or inequality as a process of answering a question:
which values from a specified set, if any, make the equation or inequality true? Use
substitution to determine whether a given number in a specified set makes an equation or
inequality true.
6.EE.6: Use variables to represent numbers and write expressions when solving a real-world
or mathematical problem; understand that a variable can represent an unknown number, or,
depending on the purpose at hand, any number in a specified set.
6.EE8: Write an inequality of the form x>c or x<c to represent a constraint or condition in a
real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c
have infinitely many solutions; represent solutions of such inequalities on number line
diagrams.
6.EE: Expressions and Equations-Represent and analyze quantitative relationships between
dependent and independent variables
6.EE.9: Use variables to represent two quantities in a real-world problem that change in
relationship to one another; write an equation to express one quantity, thought of as the
dependent variable, in terms of the other quantity, thought of as the independent variable.
Analyze the relationship between the dependent and independent variables using graphs
and tables, and relate these to the equation. For example, in a problem involving motion at
constant speed, list and graph ordered pairs of distances and times, and write the equation
d = 65t to represent the relationship between distance and time.
8.F:Functions-Use functions to model relationships between quantities
8.F.5: Describe qualitatively the functional relationship between two quantities by analyzing
a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a
graph that exhibits the qualitative features of a function that has been described verbally.
Day 8-10:
Big Math and Fries*4
Obje ctive:
Students will mathematically analyze the food they eat, identify the relationship between
nutrients and the calories, and perform calculations, including percents and conversions.
Students will also create functions to represent the conversions between nutrients and
calories.
Essential Questions:
Were you able to stay under 30% for total calories from fat? Do you feel that you designed a
healthy day of eating? What steps did you take in order to meet the requirements of 2,000
calories total and a 40-30-30 ratio? If you were not able to meet the Zone Diet requirements
of 40-30-30, could you tweak a few items to change that? If so, which items would you
change and how does that improve your carbohydrates-protein-fat ratio for the day? How
could you write a function that could be used to determine if you were able to stay under
30% for total calories from fat?
Activities:
Day 8:
Students will design a day’s worth of meals strictly from McDonald’s. Students should use
the zone diet as a guide to pick menu items.
Day 9 :
Students will organize meals on worksheets and convert between food weight and calories.
Students will interchange fractions, decimals and percents for all three nutrients (fat, protein
and carbohydrates).
Day 10 :
Students will analyze the meals they choose based on the zone diet. Students choose the
item/meal that best fits within the zone diet. Students will create functions and substitute
values in order to determine if their items fits within the zone diet. Students will present
their findings in small groups/whole class.
4
adapted from illuminations.nctm.org
Standards:
7.RP: Ratios and Proportional Relationships-Analyze proportional relationships and use them
to solve real-world and mathematical problems.
7.RP.3: Use proportional relationships to solve multi-step ratio and percent problems.
Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees,
percent increase and decrease, percent error
8.F: Functions-Use functions to model relationships between quantities
8.F.4: Construct a function to model a linear relationship between two quantities. Determine
the rate of change and initial value of the function from a description of a relationship or from
two (x, y) values, including reading these from a table or from a graph. Interpret the rate of
change and initial value of a linear function in terms of the situation it models, and in terms
of its graph or a table of values.
Day 11-13:
New-tritional Info*5
Obje ctive:
Students will calculate the rate of calories per minute burned for different exercises, for
people with different weights. Students will determine the relationship between weight and
calories burned. Students will rewrite nutritional labels so that energy is described not just in
calories, but in how many minutes of different activities will be fueled by a given food.
Students will create a function to represent the relationship between weight and calories
burned.
Essential Question:
Will a professional basketball player burn off a double quarter pounder extra value meal in a
single game?
Activities:
Day 11:
Start with a brief commercial of LeBron James eating a Big Mac and then starting and being
challenged to a game of hoops. How long would he have to play in order to burn it off?
Students will brainstorm what they need to know in order to solve the problem. Give
students formulas for rate of calories burned for different physical activities (using examples
of celebrities).
Day 12 :
Restaurants are required to list nutritional information, including the number of calories in
each item. But does anyone actually know what those calories mean, and what if there were
better ways to contextualize them? Students will translate those calories into the minutes
that it would take to burn them off and use that to rewrite nutritional labels.
Day 13:
Students will design their own product labels using minutes of activities necessary to burn
off instead of calories. Students will create functions to represent the relationship between
minutes of activities and calories burned. Students will present their product to the class.
5
*adapted from mathlicious.com
Standards:
7.EE: Expressions and Equations- Solve real-life and mathematical problems using
numerical and algebraic expressions and equations.
7.EE.3: Solve multi-step real-life and mathematical problems posed with positive and
negative rational numbers in any form (whole numbers, fractions, and decimals), using tools
strategically. Apply properties of operations to calculate with numbers in any form; convert
between forms as appropriate; and assess the reasonableness of answers using mental
computation and estimation strategies. For example: If a woman making $25 an hour gets a
10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new
salary of $27.50. If you want to place a towel bar 9¾ inches long in the center of a door
that is 27½ inches wide, you will need to place the bar about 9 inches from each edge; this
estimate can be used as a check on the exact computation.
7.EE.4: Use variables to represent quantities in a real-world or mathematical problem, and
construct simple equations and inequalities to solve problems by reasoning about the
quantities.
a.
Solve word problems leading to equations of the form px + q = r and p(x ÷ q) = r,
where p, q, and r are specific rational numbers. Solve equations of these forms fluently.
Compare an algebraic solution to an arithmetic solution, identifying the sequence of the
operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its
length is 6 cm. What is its width?
b.
Solve word problems leading to inequalities of the form px + q > r or px + q<r, where
p, q, and r are specific rational numbers. Graph the solution set of the inequality and
interpret it in the context of the problem. For example: As a salesperson, you are paid $50
per week plus $3 per sale. This week you want your pay to be at least $100. Write an
inequality for the number of sales you need to make, and describe the solutions.
MA.4.c.Extend analysis of patterns to include analyzing, extending, and determining an
expression for simple arithmetic and geometric sequences (e.g., compounding, increasing
area), using tables, graphs, words, and expressions.
8.F: Functions-Define, evaluate, and compare functions.
8.F.1: Understand that a function is a rule that assigns to each input exactly one output. The
graph of a function is the set of ordered pairs consisting of an input and the corresponding
output.
Day 14
Review
-Review/ Post-Test