Problem of the Day #8 April 2, 2020

Grade 6: A survey indicated that for every 3 students who use a laptop 5 students use an iPad. If there are 48 students overall, how many use and iPad??

Grade 7: There are 30% more boys than girls enrolled in virtual school right now. If there are  920 students total, how many girls are there?

Grade 8: The sum of 4 consecutive integers is 118. What is the smallest integer?

Algebra: It takes 45 minutes for 3 people to wash 5 cars. How long will it take 9 people to wash 12 cars? 

Geometry: A cylinder has a radius of 4 inches and a height of 6 inches. It is filled with water to a height of 5 inches. If we drop a cube with a volume of 50 cubic inches into the cylinder, will the water flow over the edge? 

Algebra 2: John and his family are thinking about discontinuing their cable TV service. Currently they pay $80 per month for basic cable and $10 for each premium channel. If they go with streaming...

April Fool’s Day Problem of the Day

Today we are going to take a short break for the typical problem of the day. The first of the April Fool’s Day problems is appropriate for all age groups. The second will test your knowledge of Algebra so is best left to 8th graders and above. I hope you enjoy these brain teaser math tricks. 

Problem 1

Write down a three digit number. The first and third digits must differ by more than 1.      735

Reverse the digits to form a second number.        537

Now subtract the smaller number from the larger.   735 - 537 = 198

Now reverse the digits in the answer you got in step three and add it to that number.    198 + 891 = 1089

Multiply the number by 1 million    1089 X 1,000,000 = 1,089,000,000

Subtract 733,361,573 from that number

1,089,000,000 - 733,361,573 = 355,638,427

Under each of the digits in your answer, write the letter which corresponds to it using the...

Problem of the Day #7 March 31, 2020

Grade 6: Solve the following equations: 

Grade 7: Solve the following equations: 

-47 + 23 =                  15 - ( -7 ) =             22 + ( -12) =        -52 - ( - 26) = 

Grade 8: Solve the following inequalities: 

Algebra: Write the equation for the line with the given characteristics: 

parallel to 2x+3y = 5 containing the point (6, -5)

perpendicular to -4x+2y = 6  with a y-intercept of 3

containing the points ( 3, -7 ) and ( 8, -12)

Geometry: Find the area of the following polygons: 

Algebra 2: Solve the following...

March 30, 2020 Problem of the Day

Grade 6: Convert the following %s into decimals and fractions in simplest form:   20%,  35%,  72%,  175%,  5%

Grade 7: Solve the following problems: 

Grade 8: Find the mean, median, mode and range of the following set of numbers: 2, 7, 11, 11, 16, 24, 29, 33

Algebra: Solve the following problems: 

Geometry: Find the midpoint and the distance between for the following points:   (5 , 7) and (-3 , 5)       (9 , 4) and (3 , 5)

Algebra 2: Solve the following inequalities:

-4 < m - 5 < 2               9 + 2b < 7  or 7 - 5b < -8 

...

March 27, 2020 Problem of the Day

Grade 6: Solve the following problems:

                                  =                 

Grace 7: Solve the following equations: 

2x - 3 = 15                                    4x + 9 = 57

Grade 8: Simplify the following expressions. Write your answers in exponential form.  

Algebra: Solve the following radical equations: 

=                                   

Geometry: solve for the variables

...

Problem of the Day March 26, 2020

Grade 6

Label the three triangles as right, obtuse or acute and equilateral, isoceles, or scalene. Find the missing side length in triangle ABC.  

Grade 7

Find the area and the circumference of the circles below: 

Grade 8

Plot the following points on the coordinate plane: ( 4 , 2 ) , ( -2 , 4 ) and 

 ( -6 , -4)

Algebra

Write the equation of the line through the points ( - 2, 4 ) and ( 6, 8 ). 

Geometry

Find the measure of the labeled angles. Name the Theorem you used to get your answer. (Alternate Interior Angles, Consecutive Angles, Corresponding Angles, Vertical Angles, Alternate Exterior Angles)

Algebra 2

Graph the following system of inequalities: 

-3x + y < 2  and 2x + y > 1

Trigonometry

Use sin, cos and tan to find the labeled sides or angles. 

Pre-Calculus

Graph the following sin function: 

March 25, 2020

Grade 6:

What it the ratio of books to boxes when you have 42 books and 7 boxes?

What is the rate? What is the difference between a rate and a ratio? Give an example of when you might use a rate? 

Grade 7:

Solve the following equations for x:

2x + 5 = 23

4x - 7 = 21

3x = 72

Grade 8:

Find a set of 4 points that solve the following linear equation: 

-3x + 4y = -2

Algebra:

Solve the following system of equations: 

2x - 5y = 6

4x + 10y = 20

Geometry:

Describe the following geometric shapes. How are they alike? How are they different?  parallelogram, rhombus, square, rectangle

Algebra 2:

Solve the following absolute value equations: 

2| 3x - 6 | = 48

| 2x + 5 | = - 23

| 5x + 7 | -6 = 41

Trigonometry: 

Give the amplitude, maximum and minimum values (range), period, vertical and horizontal shift of the following sin function:

Pre-Calculus

Find the sum, difference, product and quotient of the following...

March 24, 2020

Grade 6

Place the following decimals in order from least to greatest: 1.02, 1.002,  102.022, 1.2, 12.02,

Grade 7

Convert the following decimals into a simplified fraction and a percent.

.04, .45. 1.25

Grade 8

Simplify the following exponential expressions: 

(2x)³, (2x²)³, (2x²)(2³x³)²

Algebra

Simplify the following radicals:

Geometry

Name the 4 triangle congruence theorems and draw and example of each.

Algebra II

Convert the following quadratic equation into vertex form: 

2x² + 16x + 12

Trigonometry

Give the values for sin and cos of the following angles: 

PreCalculus

Find the vertical and horizontal asymptotes of the rational function without graphing:

Answers: 

Grade 6: 1.002, 1.02, 1.2, 12.02, 122.022

Grade 7:

Grade 8:  8x³, 8x⁶, 128x⁸

Algebra:

Geometry: see this website https://www.appohigh.org/ourpages/auto/2014/11/17/63624959/Congruent%20Triangles.pdf

Algebra II:  2(x + 4)²...

March 23, 2020

Grade 6 

23.14 + 1.02 = ?

Grade 7

Grade 8

Categorize the following Real numbers as : Natural, Whole, Integer, Rational and Irrational. Make sure to include every appropriate category.

Algebra 

Add: 

Geometry

Describe the side length and angle measurements for equilateral, isosceles and scalene triangles.

Algebra II

Find the vertex and direction of opening for the following parabola.     

Trigonometry

You have a right triangle ABC with sides a and b and hypotenuse c. The length of side a is 6. The length of side b is 8. Find the length of side c and set up the 6 trig ratios (sin, cos, tan, csc, sec and cot) for angle A

PreCalculus

Write the transformation of the graph of y = x²  shifted right 4 units, up 2 units and reflected over the x axis.

Answers

Grade 6:     24.16

Grade 7:    

Grade 8:  -19 real, rational, integer

...

Each day the news brings more unprecedented closures including our schools. How can you help your student stay on track, or maybe even gain ground during this time? 

Fortunately, many students are already familiar with some form of online learning. The challenge is to help them stick to a schedule. We all do it. We get an unexpected snow or hurricane day and all we want to do is relax and enjoy. This closure is different. It isn’t a day to two. So far in Florida we are looking at two weeks and there is a very real possibility that it may be longer than that. 

It is critical that your student continue as though he or she was still attending school. Set up a work area and time expectations. Be specific! Don’t just say, “Go do your schoolwork.” Help them set expectations for how long assignments will take and prepare a schedule from there. I find it helpful to set time blocks rather than task completion. For example: 

8:00 - 9:15  Math...