MATH 3803 – JOURNAL ENTRIES
1. Explain in your own words what it means to generalize a growing pattern.
Provide an example with your explanation.
2. Conjecture: Multiplying a number by 4 is the same as doubling the number and
then doubling the result. If true, justify. If false, provide a counterexample. b)
Why do you believe that it is important for elementary students to make and
justify conjectures?
3. a) Compare and contrast Ricardo’s response with Gina’s response. b) Use Gina’s
reasoning to determine whether the following is true or false. Explain your
reasoning.
142 + 257 = 145 + 254
4. What is relational thinking? Provide an example with your explanation.
5. Compare and contrast the following two responses below for solving the equation
4(m – 6) = 28. Which of the responses exhibits relational thinking? Explain your
thinking.
Response A: First, I divided both sides by 4. This left me with m – 6 = 7.
Next, I added 6 to both sides of the equation and got m = 13. The solution is 13.
Response B: I looked at the equation and asked myself 4 times what is 28.
Well that is 7 so I know that whatever is in the parentheses has to equal 7. So I know
that m is 13 because 13 minus 6 is 7.
6. Use pictures and words to describe how to solve the equation 3(x + 4) = x + 20
using Hands-On Equations.
7. Create a problem that can be represented with a system of equations (similar to
the moles, lizards, and skunks problem from class). Your problem should have
three unknowns. After creating your problem, you should demonstrate how to
solve the problem first using manipulatives and then by substitution.
8. Provide and example of an inequality that when graphed would have an open
circle. Graph your inequality. Explain what the open circle means in terms of
your solution set.
9. Explain in your own words when it is necessary to change the inequality symbol.
Include an example with its solution.
10. Benny’s Burgers (see pg 49 ½ from course packet).
10.5 Explain the difference between a line that has zero slope and a line that has no
slope. Include an example equation with its graph for each.
11. Explain in your own words why it makes sense that the point of intersection is the
solution to a system of equations.
12. Consider the sets below. Explain why A is not a function and why B is a
function.
A = {(1,2), (1,3), (1,4)}
B = {(2,1), (3,1), (4,1)}
13. Create a “Guess my Number” problem. Show algebraically why it works.
13.5 Explain why a number raised to the zero power is one.
14. Compare and contrast the processes of adding with base-10 blocks and adding
with algebra tiles.
14.5 What is the area model for multiplication? Use pictures and words to explain
how to use the area model to solve each of the following:
a. 4 x 5
b. 11 x 13
c. (x + 1)(x + 3)
15. Explain how to factor 2 x 2  x  3 . You may choose to use either the algebra tiles
or the box in factoring this trinomial.
15.5 Compare and contrast f(x) = 2x and f(x) = x 2 . Give at least 3 ways they are
alike and 3 ways they are different.
16. “Algebra & Me – Chapter 2” – Write a thoughtful reflection about your
experience in this class. Be sure to address the following:
a. What have you learned?
b. How have your views about algebra changed, if at all?
c. What role will algebra play in your future classroom?