# data[].attributes.body
First I wrote down what each letter represented and I then broke down each equation.
AD: 1 group of 5 and 4 ones
1x5+4=9
BD: 2 groups of 5 and 4 ones
2x5+4=14
CB: 3 groups of 5 and 2 ones
3x5+2=17
CD: 3 groups of 5 and 4 ones
3x5+4=19
DD: 5 groups of 5 and 4 ones
4x5+4=24

# data[].attributes.body
Using the formula for CB, I figured out the equations to be the following:

AD is 1 group of 5 + 4 ones or
1 x 5 + 4 = 9

BD is 2 groups of 5 + 4 ones or
2 x 5 + 4 = 14

CB is 3 groups of 5 + 2 ones or
3 x 5 + 2 = 17

CD is 3 groups of 5 + 4 ones or
3 x 5 + 4 = 19

DD is 4 groups of 5 + 4 ones or
4 x 5 + 4 = 24

# data[].attributes.body
I had to write out not only the key for what each number means in x-mania but I also had to write out each individual step discussed to fully grasp the concept. It took me a few minutes to understand base 5 because my brain automatically jumps to a base 10.

AD: 1 group of 5, and 4 ones, (1x5)+4 = 9
BD: 2 groups of 5 and 4 ones, (2x5)+4+ 14
CB: 3 groups of 5 and 2 ones, (3x5)+2= 17
CD: 3 groups of 5 and 4 ones, (3x5)+4=19
DD: 4 groups of 5 and 4 ones, (4x5)+4=24

# data[].attributes.body
I used the formula given and plugged in the numbers into the new equations.

AD: 1 group of 5 and 4 ones, which is 1 x 5 + 4 = 9
BD: 2 groups of 5 and 4 ones, which is 2 x 5 + 4 = 14
CB: 3 groups of 5 and 2 ones, which is 3 x 5 + 2 = 17
CD: 3 groups of 5 and 4 ones,
which is 3 x 5 + 4 = 19
DD: 4 groups of 5 and 4 ones,
]which is 4 x 5 + 4 = 24

# data[].attributes.body
Part 1:
I wrote the key first and then took some time getting used to the idea of base 5 but once I began it got easier and easier.
AD= (1*5)+4= 9
BD= (2*5)+4= 14
CB= (3*5)+2= 17
CD= (3*5)+4= 19
DD= (4*5)+4= 24

# data[].attributes.body
I like many others had to write out the equation first to be able to truly understand this new concept which makes me realize why it is so important to teach expanded form to kids before this assignment I thought it was trivial, now I understand!

AD- 1 group of 5, and 4 ones- 1x5+4= 9
BD- 2 groups of 5, and 4 ones- 2x5+4= 14
CB- 3 groups of 5, and 2 ones- 3x5+2= 17
CD- 3 groups of 5, and 4 ones- 3x5+4=19
DD- 4 groups of 5, and 4 ones- 4x5+4= 24

# data[].attributes.body
Like a few others, I wrote out the equation in words first.  It just helped me keep it organized.

AD is 1 group of 5 and 4 ones
BD is 2 groups of 5 and 4 ones
etc..etc..

Then I wrote the number sentence...
AD= 1 * 5 + 4
AD= 9

BD= 2 * 5 + 4
BD= 14

CB= 3 * 5 + 2
CB= 17

CD= 3 * 5 + 4
CD= 19

DD= 4 * 5 + 4
DD= 24

# data[].attributes.body
I had to write out a key so that I would not get confused

0=0; A=1; B=2; C=3; D=4

AD= (1x5)+4= 9
BD=  (2x5)+4=14
CD= (3x5)+4=19
CB= (3x5)+2= 17
DD=(4x5)+4= 24

I had to keep remembering that 5 is our 10.

# data[].attributes.body
Based on the idea that A=1, B=2, C=3, D=4---

AD (1 group of 5 and 4 ones); (1 x 5) + 4 = 9

BD (2 groups of 5 and 4 ones); (2 x 5) + 4 = 14

CB (3 groups of 5 and 2 ones); (3 x 5) + 2 = 17

CD (3 groups of 5 and 4 ones); (3 x 5) + 4 = 19

DD (4 group of 5 and 4 ones); (4 x 5) + 4 = 24

# data[].attributes.body
I had to write out a key so I could then figure out the equations.

AD= 1 group of 5 and 4 ones
(1X5) +4=9

BD= 2 groups of 5 and 4 ones
(2x5) + 4 =14

CB= 3 groups of 5 and 2 ones
(3x5)+ 2 =17

CD= 3 groups of 5 and 4 ones
(3x5)+ 4 =19

DD= 4 groups of 5 and 4 ones
(4x5)+4= 24

# data[].attributes.headline
Joy Scalera I had to break each one down . I started by creating a key for what each number represented

# data[].attributes.subject
Joy Scalera I had to break each one down . I started by creating a key for what each number represented

# data[].attributes.body
0 = 0 | A = 1 | B = 2 | C= 3 | D = 4

AD = 1 group of 5 plus 4 ones      = 1 * 5 + 4 = 9

BD = 2 groups of 5 plus 4 ones    = 2 * 5 + 4 = 14

CB = 3 groups of 5 plus 2 ones     = 3 * 5 + 2 = 17

CD = 3 groups of 5 plus 4 ones     = 3 * 5 + 4 = 19

DD = 4 groups of 5 plus 4 ones    = 4 * 5 + 4 = 24

# data[].attributes.body
Based on that idea, describe how you would write an equation like the one above for CB to represent these XMania numbers: AD, BD, CB, CD, and DD.

AD= 14= 1 of 5 and 4 ones= 1X5+4=9

BD= 24= 2 of 5 and 4 ones= 2X5+4=14

CB= 32= 3 of 5 and 2 ones= 3X5+2=17

CD= 34= 3 of 5 and 4 ones= 3X5+4=19

DD= 44= 4 of 5 and 4 ones= 4X5+4=24

Part 3: Reflection questions

1) What was confusing or tricky about the X-Mania math?

You had to get the patterns and representations correct.

2) What is the connection between this task and what Grade 1 and 2 students work with in mathematics classrooms?

Students in grades 1 and 2 are using tens frames and groupings of ten. They have to distinguish between groups of ten and ones.

3) Why do you think place value and the value of numbers is such a difficult component for a lot of students in Grades 1 through 3?

Well with each place value there is a new rule added. Students have to build on prior knowledge. They have to remember these rules with each place value they learn. They have to recognize and retain these rules when solving groupings of numbers.

# data[].attributes.body
To not confuse myself, I first wrote out in words what each letter would represent in the equations...so first I had
AD as 1 group of 5 and 4 ones...5+4=9
BD is TWO groups of 5 plus 4 ones...5, 10..14.
CB is THREE groups of 5 plus 2...5, 10, 15..17.
CD is THREE groups of 5 plus 4..5,10,15,...19.
and DD is FOUR groups of 5 plus 4...5, 10, 15, 20..24.

# data[].attributes.body
I used the CB formula and plugged it into the rest.  Using A=1, B=2, C=3 and D=4 with the formula of CB: 3 groups of 5 and 2 ones, which is 3 x 5 + 2 = 17.
AD: 1 group of 5 and 4 ones, which is 1 x 5 + 4 = 9
BD: 2 groups of 5 and 4 ones, which is 2 x 5 + 4 = 14
CB: 3 groups of 5 and 2 ones, which is 3 x 5 + 2 = 17
CD: 3 groups of 5 and 4 ones,
which is 3 x 5 + 4 = 19
DD: 4 groups of 5 and 4 ones,
]which is 4 x 5 + 4 = 24

# data[].attributes.body
To be able to write these equations to understand what I was doing I had to first write out what the symbols meant in words and and then correlate them with the numbers.

AD:
1 group of 5 + 4
(1x5)+4= 9

BD:
2 groups of 5 + 4
(2x5)+4= 14

CB:
3 groups of 5 + 2
(3x5)+2= 17

CD:
3 groups of 5 + 4=
19

DD:
4 groups of 5 + 4
(4x5)+4= 24

# data[].attributes.body
It was really difficult for me to abandon the notion of 10 being the base of the numerical system, and adapt to it being 5, as in this scenario. However, once I worked on several "numbers," I began to get the hang of it and got into a groove. I definitely see how repetition and practice are SO important, and that you need to ensure a student understands one digit numbers prior to moving onto two digit numbers, and develop an understanding of two digit numbers prior to moving onto 3 digit numbers. Once I got into the mindset that 5 is similar to our 10 and 25 is similar to our 100 in this mathematical system, it became much easier for me to work with the number and realize that:
AD = 1 group of 5 and 4 ones = 4x5+4 = 9
BD = 2 groups of 5 and 4 ones = 2x5+4 = 14
CB = 3 groups of 5 and 2 ones = 3x5+2 = 17
CD = 3 groups of 5 and 4 ones = 3x5+4 = 19
DD = 4 groups of 5 and 4 ones = 4x5+4 = 24

# data[].attributes.body
how did you get