Appendix C: Problem Sets
Numerical Expressions
Write the numerical expression that represents the computation
1. Take 5, multiply by 2, add 2, divide by 3 then add 6.
2. Take 10, divide by 2, multiply by 3, subtract 7 and double.
3. Take 7, subtract 1, multiply by 2, divide by 6, add 3 and triple.
4. Take 88, divide by 11, multiply by 2, divide by 4, add 3, subtract 6.
5. Take 63, divide by 9, multiply by 2, divide by 14.
Write the recipe for computation of the given expressions
Number Tricks
Students choose numbers, teacher guesses starting numbers from the given results.
1. Choose a number. Add 6. Multiply by 3. Subtract 10. Multiply by 2. Add 50. Divide by 6. What is the result?
2. Choose a number. Multiply by 3. Subtract 4. Multiply by 2. Add 20. Divide by 6. Subtract your starting number. What's your result?
3. Choose a number. Add 5. Multiply by 2. Subtract 7. Add 1. Divide by 2. Subtract 2. What's your result.
1. Choose another number and do the same trick from number 3. What is your result? What do you notice? Do you think this works for any number?
2. Choose a number. Add 3. Multiply by 2. Add 7. Subtract 15. Add 2. What is your result?
Scenario Problems
1. Ricky has 3 fewer apples than John. Let j stand for the number of apples that John has. Write an expression for the number of apples that Ricky has.
2. Sara has 6 more dresses than Stephanie. Let d stand for the number of dresses that Sara has. Write an expression for the number of apples that Stephanie has.
3. Louis has double the amount of red trucks that Maia has. Define a variable and write an expression for the number of trucks Louis has.
4. Sean has 14 more pieces of paper than Brian. Define a variable and write an expression that represents the number of pieces of paper Sean has. Write an expression for the number of pieces of paper Brian has.
Combining Expressions
1. Donald counts the number of quarters he has in his piggy bank. He has 25 more quarters than his brother Robert. If r is the number of quarters Robert has, write an expression that represents the number of quarters that Robert and Donald have together.
2. Alanna has 10 more pairs of shoes than her sister Greta. They have the same size feet so they like to share shoes. Define a variable and write an expression that represents the number of shoes Alanna has, write an expression for the number of shoes Greta has and write an expression for the number of shoes they have together.
3. Marcelo has eaten 10 fewer burritos then Andrew. Define a variable and write an expression that represents how many burritos they have eaten combined.
1. Challenge: Shannon has 3 fewer dogs than double Lesley's. Define a variable and write an expression that represents how many dogs they have combined.
Reading and Writing
Pairs switch off between reading and writing.
1. Take a number. Multiply by 2. Subtract 5. Multiply by 9. Subtract 3.
2. Take a number. Multiply by 2. Add 5. Multiply by 2. Add the number.
3. Take a number. Multiply by 2. Add 1. Multiply by 3. Add 13.
4. 2(x + 3) – 6
5. (4(3 – (x – 1))) – 2
Evaluating/Simplifying
Evaluate the given expressions at the given values.
Nine Rules of Arithmetic
1. Does 3+10=10+3? What rule justifies your answer?
2. Does 3+(6+4)=(3+6)+4? What Rule justifies your answer?
3. What is 3+(-3)=? Explain why.
4. What is 3+0=? Explain why.
5. Does 3•2=2•3? Show your reasoning.
6. Does (4•5)•6=4•(5•6)? Show your reasoning.
7. What is 3x(1/3) = ? Explain why.
8. What is 3•1=? Explain why.
9. What is 3(4+x)=? Show your reasoning.
Simplifying Expressions
Simplify the following expressions. Make sure to give a reason for each step you perform.
Evaluate the original expressions above AND the simplified form at x=1, 2, 3, 4, 5. If you do not get the same answer for the original and simplified form, you have simplified wrong and you must go back and fix your simplified form.
Equations
Solve for the variable. Make sure to give a reason for each step you perform. Remember you can check your solutions.
Equation Word Problems
Define your variables. Write an equation based on the problem and solve for the given variable.
1. John had some apples and today he bought 4 more apples. Now he has seven apples. How many did he have?
2. John bought 3 packages of donuts. He opened them up and counted them and there was a total of 24 donuts. How many donuts were in each package?
3. John has 4 packages of donuts and 5 leftover donuts not packaged. In total he has 21 donuts. How many donuts are in each package?
4. There are 33 students in the class. There are 7 more girls than boys. How many boys are there and how many girls are there?
5. The local commuter train has three passenger cars. When it is full each car holds p people. In addition to the passengers, the train has 8 workers. Write an equation to represent the total number of people the train can hold if when completely full it holds 176 people. How many passengers fit in each car?
6. Tony rode his bike some amount of miles. If Katie rode 10 less than twice the number of miles Tony rode. How many miles did Katie ride?
7. If Oceana has x students and Terra Nova has 200 more than 2 times the amount of students Oceana has, how many students go to each school?
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