Group 1 - Names€¦ · Group 10 - Names: To share your group idea, you can use the tools on the toolbar to draw on this slide and add text take a picture of one of your papers and

Group 1 - Names: To share your group idea, you can

● use the tools on the toolbar to draw on this slide and add text

● take a picture of one of your papers and add it to the slide

● hold up a picture to your camera and explain off of your own work





I multiplied each minute by four then added one to determine where the pattern would be , because it is growing by four but you also have to account for the first dot.





If we add 4 more for each additional minute, it is easy to put a quick equation together. It would also be fairly easy to put in a diagram of the growing pattern for younger users.





At minute marker 4, the dots would be at 17, at 19 minutes, 77.At t=0, there is one dot, at t=1, there are 5, so formulaically a student could reason that this pattern is mathematically represented by 4t + 1 = x (where t is time in minutes, & x is the # of dots present at that time)

t=0, 1

dot

prese

nt t=1, 5

dots

presen

t

+4 per

minut

e





I came up with y=1+4x, where y is the number of dots and x is the number of minutes that have gone by.

This connects to the picture because we start with 1 dot, and add 4 dots for each minute that goes by.

4x + 1 = y

X is the number of minutes

We must add one because at the beginning there is one dot initially. We need to multiply the number of minutes by four since the pattern grows by 4 each minute.





(4 branches) x (number of minutes) + (1 center dot) = total dots

● I noticed every pattern has a center dot.● The pattern increased by 4 each time, because each branch added one. ● So if each branch has the same number of dots as minutes and there is a center dot

Equation: 4x+1 = total dots, where x stands for how many minutes has passed.

After 4 min: 4(4) + 1 = 17 dotsAfter 19 min: 4(19)+1 = 77 dots





Every picture begins with one dot (in the middle), then each minute, adds 4 dots on the end of each branch.1 + 4m m = # of minutes

Time in minutes

# of Dots

0 1

1 5

2 9

3 13





I made a table with the number of minutes in one column and the number of dots in the other column. I noticed that when the number in the first column increased by 1, the number in the second column increased by 4.

Group 9 - Names: Debbie To share your group idea, you can




I see four dots added for each minute so the total for four minutes would be 4 * 4 would be the number of dots added for the four minutes plus the one at the start, making a total of 17 dots at the fourth minute. Then for the nth minute it is 4 * n + 1.





The pattern begins with a single dot at zero minutes. The second minute has 9 dots. Given the formula 4x+1, we can figure out that at 4 minutes there would be 17 dots and 19 minutes would have 77 dots. I can see the increase of four dots with 0=1 dot, 1 min = 5 dots, and 2 mins = 9 dots; 5-1=4 dots, 9-5=4 dots





4n+1N being the number of minutes

© 2019 Teachers Development Group

Assuming the sequence continues in the same way, how many dots are there at 4 minutes? 19 minutes? Any number of minutes?

● Use our noticings and wonderings to make and justify conjectures about what is true about the number of dots at any time (minutes).

● Be sure to connect your ideas to the picture and explain your reasoning.

● “At ______ minutes, there are ________dots because_______.”


Working with Public Records of Our Mathematical Thinking:

Noticings & Wonderings• Where will the pattern be in 10

minutes?• What does this pattern represent?• Is the pattern going to double?• Will be any other colors or shapes?•

● Beginning of a pattern● Increases by 4● The pattern is over time● Grows diagonally from the one dot● All was black and circular● Formed an “x”● The middle one looks like a dice● It is expanding from left to right


Your Group Challenge1. Use a go-around protocol to share how your

solution connects to the picture (1 minute each)2. Select one strategy to develop on your slide.3. Be certain you connect your solution to your visual to

justify your answer.4. Once you have developed one strategy, try another if

you have time.

Extra copies of the dot task

Documents

Group 1 - Names€¦ · Group 10 - Names: To share your group idea, you can use the tools on the toolbar to draw on this slide and add text take a picture of one of your papers and