Objective: Problem Solving Activities

Objective: Problem Solving Activities AIM: -SWBAT extend their knowledge of Algebra, pattern, and number sense to problem-solving.

Materials: (none)

Do Now (5minutes): The sequence 2, 3, 5, 6, 7, 8, 10, 11, ... , 99 consists of all positive integers between 1 and 100 that are not squares. How many terms are in this sequence?

Mini-Lesson (10-15 minutes) Connection—why is this skill/strategy/concept important? These types of problems make use of the math we have been using all year, but now we are not given/taught any specific strategy to arrive at a solution.

What is the skill/strategy/concept you’re teaching/modeling? Using math skills we have already developed and applying them to more abstract-looking situations.

How will you model/teach it? I will give a few minutes for students to try the do now. At that time, some student may present his or her strategy on this. I will also contribute my own strategy: Let us think about all the square numbers between 1 and 100: 1, 4, 9, 16, 25, 36, 48, 64, 81, 100. There are 10 of these. That means there are 100 – 10 = 90 terms in the sequence described.

This is given as an example to get students thinking about how they can work backward or think abstractly to arrive at answers for these kinds of problems.

How will the students practice the new skill/strategy/concept with your guidance? (See “Group activity” below)

How does the new skill apply to what they’re doing in the unit? Each problem can be solved using algebra or geometry strategies students have learned in 8th grade. Students are now using their previous knowledge and applying it in a different context.

Guided Activity: I will give my explanation as to how I would go about solving the do now, in an effort to get students to start thinking “outside the box.”

Independent/Group Activity: In groups, students will work on problem-solving activities pulled from NCTM’s Mathematics Teaching in the Middle School. At the end of the class period, some students will present some of the solutions they were able to come up with. Any student who presents a solution to the class will be offered some extra credit.

Adaptations (For Students With Learning Disabilities): I will circulate the room and offer hints on some of the problems that students may be struggling with.

Extensions (For Gifted Students): Ask students who have solved a problem to try to solve the same problem using a different strategy.

Assessment: Student’s presentations at the end of class will indicate how well they understood the concepts they are speaking about. I can also look around the room and see how many problems each student is able to complete. However, problem-solving can be difficult for many students and so it can be the case that a capable math student will only come up with solutions for 1 or 2 problems (which can be frustrating). This is okay, as long as it is clear that students are actively thinking about how to arrive at solutions.

Closure: Some students will present their solutions to some of these problems. After each solution is presented, I will ask the class if any one else used a different strategy to solve the same problem. It is often the case that students will come up with unique, mathematically-rich solutions, some of which that even a teacher may not have thought of.

Name: ______Date: ______Class: ______1) Without rearranging any digits, insert one multiplication symbol () into the following expression to obtain the greatest possible product:

1 2 3 4 5

2) Based on the box of numbers below, determine the missing value in the bottom-right box.

4 9 11 6 8 12 13 16 27 19 26 43 23 7 28 31 47 ?

3) Continue the pattern by listing the next five terms in the sequence below:

17, 8, 25, 7, 32, 5, 37, 10, 47, 11, 58, 13, 71, 8, __, __, __, __, __

4) Paige has exactly $5.60 in U.S. quarters, dimes, and nickels. How many of each coin does she have if she has the exact same number of each type of coin?

5) Dates can be abbreviated using two-digit numbers for the month and day. For example, March 15 can be written as 3-15. A palindrome date is a number, with the hyphen removed, that looks the same whether the digits are read from left to right or from right to left. March 3, December 1, and December 21 are palindrome dates because their corresponding numbers of 33, 121, and 1221 are palindromes. List all the palindrome dates.

6) An office building has 36 stairs between the first and third floors. If any two floors have the same number of stairs between them, how many stairs must a visitor climb to reach the sixth floor?

7) How many numbers between 9 and 100 exist such that the product of the digits is greater than the actual number?

Name: ______Date: ______Class: ______1) Here are three “Sierpinski triangles.” Draw the next two triangles in the sequence.

2) In the alphabetic pattern

ABBCCCDDDD...,

A is in the first place, B is in the second and third places, C is in places 4- 6, and D is in places 7-10. If the pattern continues, in what place would the first N land?

3) If the consecutive odd counting numbers are arranged as shown, what will be the middle (center) number in the 11th row?

4) The 30 students in a class line up in a row. The largest number of consecutive boys in a row is 4. What is the maximum number of boys in the class?

5) Find a number x to make this statement true:

(x ÷ 32) − 4 + 3 × 23 = 36

6) You and your family leave for a two-week vacation. Your little brother accidentally left the bathroom faucet dripping. If the water drips once every second, how many times will the water drip in (a) one hour, (b) one day, and (c) the whole time that you are on vacation? If the water leaks at a rate of a gallon per hour, how much water will be wasted while you are on vacation? If the cost of water is $0.01 per gallon, how much money will be wasted?