Reflection on 3 Act: Lego Slide

We combined our first grade classrooms today for the 3 Act lesson I just completed on comparing lengths.  This was a different format than we had used before for 3 Act lessons.

I thought this was the perfect time to try out the fill in the blank feature on Nearpod (see below).  In Nearpod, I type in the sentences I want to use and highlight the words that should be in the word bank.  When the students see the question, the boxed words show up in the word bank at the bottom of the screen and they slide them to their correct positions.  2016-04-22 15_05_35-Nearpod Lessons_ Download ready-to-use content for education

Students shared iPads in partner groups to discuss the lesson.

The more we introduce 3 Act tasks in first grade the more focused they become, but we often need to funnel student questions sometimes when we ask, “What do you notice, what do you wonder?” so that they focus their attention on how the video relates to math questions.

It was really interesting to see and hear students during the Act 2 video, because they choral counted the length of each box as they were laid out in the video.

We made an anchor chart for them to refer back to during the prove it portion of Act 2 that looked like this:

IMG_4971.JPG

The question we presented for Act 2 was: “Which box is the shortest?  Which box is the longest?”

As students were drawing and reasoning about which box was shortest and which was longest, we noticed that many groups were struggling with recording their thinking.  The act of organizing their information into a drawing or equation that would answer the question was causing a lot of great conversation between partnerships.  The two first grade teachers and I joined groups and probed for specificity in their solutions.  Many students drew a solution and submitted it quickly without checking and discussing with their partners to agree on what to submit.  This brought up a great teaching point on what types of checks we should perform before submitting answers.

When we asked groups to share their thinking, we started with this one:

2016-04-22 13_17_47-Nearpod - Reports I started by asking, “I’m a little confused about this one, is anyone else having trouble with this drawing?”  Several students raised their hands and I asked them to share.  One student said, “there aren’t any green or red boxes.  They are blue, white and yellow.”

I said, “yeah, that’s what I was having trouble with.  What was your thinking here?”  One of the students from this partnership said, “that’s the Legos.”  I said, “oh the red and green are the Legos.  Does anyone have any questions for them about that?”  A student raised his hand and said, “we were measuring the boxes, not Legos.”  So I replied, “does this picture tell us which box is shortest or longest? ”  The students said “no.”  I said, so how could they make this better so that they answer all parts of the question?” Students: “draw the blue, white and yellow boxes.”  “Okay, that sounds like that might be a good strategy.  Do you agree that would help your audience see your thinking?”2016-04-22 13_17_02-Nearpod - Reports

The next group that shared, showed the drawing to the right.  When I asked them about their drawing, they said, “The yellow box is the longest.”   I said, “oh, what is this in here?”  The student said, “that is the 16 because it is 16 long.”  I said, “oh so you labeled it so we would know how long it was. Are these the legos that were used to measure?”  Student: “yes.”  Me: “Okay, can you tell us more about your picture?”  Student: “No.”  Other teacher, “you said you drew that box over there for something.  What is that?”  Student: “Oh, that is the white box.  It’s the shortest.”  Me: “So what do we think of this drawing?  Does it answer the question?  How could this drawing be improved to prove their thinking?”2016-04-22 13_10_42-Nearpod - Reports

The drawing on the left is the next drawing.  It is very similar to the one directly underneath it.  When the students showed this drawing, I said, “tell me about your drawing.  I see some numbers.  Are these the boxes?”  Student: “yes, the yellow is the longest.” Me: I see a 16 in both the yellow and blue, tell me about that.”  Student: “well the blue is not supposed to be 16, it is 13.”  Me: “Okay, so you just labeled that incorrectly?  Which one is the 2016-04-22 13_19_32-Nearpod - Reportsshortest?”  Student: “the white one.  It is only 9.”  Me: “9 what?”  Student, “9 legos long.”  “Oh, okay.  I see the numbers and I see how you labeled the yellow one long.  That helps me to know your thinking.  What could you add to the white box to let me know your thinking about that?”  Student: “shortest.”  Me: “yes, that would help me to know, how about you class?  Would that help tell us know which is the shortest?”

We always wish we had time to look at all of the solutions more in depth, but by this time our 1st graders attention spans have reached their limit.  Our plan is to start using peer conferencing for each group to have the opportunity to share with another group and receive feedback, but first we have to set the expectations and the protocols so that they have an idea of what descriptive feedback looks and sounds like.  The conversations we hear kids having with each other elevate each time we present them with a new 3 Act task.

Below are the remaining solutions.  Look through the drawings and determine what questions we might ask to help students identify and think through precision and detail when solving problems.
2016-04-22 13_11_21-Nearpod - Reports

2016-04-22 13_12_02-Nearpod - Reports
2016-04-22 13_18_12-Nearpod - Reports2016-04-22 13_18_26-Nearpod - Reports
2016-04-22 13_18_53-Nearpod - Reports
2016-04-22 13_19_47-Nearpod - Reports

Making Surface Area Visual

One of the students I tutor is a sixth grade girl.  When she came to me,
she was struggling with math anxiety.  When I gave her the Math Add+Vantage assessments it was apparent that she had very little number sense.  She struggled with composing and decomposing numbers with the help of structures such as ten frames and rekenreks and she had almost no concept of subtraction.  She was TERRIFIED of math and when I asked her a question she would just start throwing out answers and correcting herself.  It broke my heart.

To begin I had to get her feeling successful in math.  For the first couple of sessions, we just worked on working slowly and talking about strategies.  We played with fraction tiles, cuisenaire rods, rekenreks, ten frames, counters, dice, etc.  We played math.  We talked about what made her nervous and what she felt like she was good.    Most of all, we spent a lot of time working on structuring to 10, to 20 and to 100 and she has made great strides.  It was apparent with her from the beginning that she had not been provided concrete practice or examples in her early math experiences.

When she was working on fractions, she depended entirely on “tricks” and sayings to remember what to do.  The “why” was missing completely.

Last week, she failed a test on surface area and volume.  Her teacher was going to let her retake it the next week.  When we met to discuss it, it became clear that she needed 3 dimensional objects to connect back to.  When I asked her how many faces were on a rectangular prism she thought it might be 4.  We worked through some problems, but she continued to have difficulty visualizing the prism and was inconsistent in her answers.

This week I came prepared to provide those experiences.  She seemed to have a pretty good grasp on area, but volume and surface area were not sound.

I realized she needed to actually see me unwrap a rectangular prism into faces.

I provided this example:Drawing SA

I brought a rectangular prism and had her touch the faces.  I had her count them and we discussed how many numbers she might have for the area of each face.  She said 6.

I then provided her with a piece of graph paper and had her draw each of the faces (and shade the area).  We discussed that two faces are identical and found them on the prism as she drew.  She labeled them as we went with length and width.Concrete SA

After she had all of the faces drawn, I asked her how she would find the surface area of each.  She added the length and width.

I said, “Count the shaded squares inside and see if that works out.”

She replied, “Oh! It’s multiplication!”

I then asked, “How many surfaces are there? “

“6.”

“So how many products will you have all together?”

“6.”

“So what do you do with all of those products.”

“Add them together?”

“Does that make sense?”

“Yes.”

“Why?”

“Because it will be the total area of all the faces.”drawing 4.png

I then had her try another problem using graph paper and asked her to try not shading the areas this time.

She was able to do that pretty easily, but she stopped drawing after four faces and I asked her how many faces she had so far.

She still struggled with the last set of faces.  We talked about which dimensions she had already used and she was able to draw the remaining two faces.  Visual.png

When she added the products I made note of some strategies we needed to look at for addition in a later lesson.

I asked her the units and she knew they were “squared” but we had to discuss how to show that in the answer.

The prior week we had talked about 2-dimensional shapes and how when we find area, the product is 2 factors which gives us units squared, but when we find volume it is a 3-dimensional shape and the product of 3 factors is units cubed.  She seemed to have retained that.

Drawing SA 3.png

Since she was having so much trouble with deciding which factors to multiply in the last two examples, I wanted to provide her an example that had two factors that were the same and see what she did with it.

This time I told her I was going to take away the graph paper, but that she could recreate it with a drawing.  I modeled the first one and then let her work on it.Representational.png

She did as predicted.  She just chose some numbers she saw and multiplied.  I asked her to identify the dimensions she was multiplying and she did, but still didn’t notice the problem of her 8 x 8 square.  I asked her to show me the two eights on the square she drew and she found her mistake.

She said, “Oh!  Now I get it!”

She continued with this example and then we moved on to a review on volume.

I asked her if she remembered the formula for volume and she said, “yes, length times width.”  I said, “isn’t that the formula we just used for area of a face?”

She said, “yeah.”volume.png

I pulled out my phone and showed her the video from the 3 Act Task, Stack Em’ Up and then drew this picture for her.  We talked about how it is three layers of 32 and she was able to tell me the formula was length times width times height.  I had her work a few problems and she did so with no problem.

I cannot stress enough the importance of making math visual for students.  This brilliant little girl has felt like a failure her whole life in mathematics because she was not given the tools to succeed.  This must not continue.  She can now solve simple subtraction problems with ease and mentally add and subtract 3-digit numbers using strategies such as compensation.  All because we took our time and connected the concrete -> visual -> abstract.

Most importantly, her attitude about math is changing.  She is more confident in her answers and she has strategies to prove it.  In my opinion, that is her greatest success!

3 Act: What Comes Next?

I was working on a graphing task for first grade with color cubes and thought they would be a great prop for number patterns.  This task addresses standard 1.OA.C.5: relating counting to addition and subtraction.

Act 1:

What do you notice?  What do you wonder?

What comes next?

Act 2:

Act 2 Colors.png

act-2-labeledAct 2.png

How many purple cubes will there be?

How many blue cubes will there be?

Act 3:

Share your strategies.

3 Act: All the Little Duckies

I was in a 2nd grade room the other day and a teacher was presenting a lesson on measurement using customary units.  Students were using rulers to measure to the nearest inch.  One of the students asked, “what if it is over 4 inches but not 5 inches?”  The teacher said, “you choose.”   I walked over and whispered, “actually let’s round up if it’s at a half and down if it’s before half because when they use rounding in 3rd grade next year, that will provide them the visual representation to refer back to.”

This really got me thinking again about the power of vertical teaming.  This teacher didn’t know that this is a common misconception in 3rd and 4th grade.  She also didn’t know many of the misconceptions around measurement.  She anticipated that they might start with something other than zero, but she didn’t know to address that in 2nd grade we are measuring units without precision and that vocabulary such as “about 5 inches” is necessary.  Or that conversations about which one to choose would be necessary.  In the task below for standard 2.MD.A.2, I hope to have students dig into discussions about which number to choose and why.  I want them to defend their reasoning and discuss which would be more accurate.  This will allow students to reason with numbers and will carry over to rounding, to estimation, and to looking for reasonableness in their answers in years to come.

The Common Core Standards specifically state in 1.MD.A.2 to ” Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.”  That is the reason that I used standard 2.MD.A.2 for this task.  In my opinion, this task is very appropriate for first grade and kindergarten students as well.  That conversation cannot happen early enough!

Act 1:

About how many ducks long is the math rack?

About how many cubes long is the math rack?

Act 2:

IMG_4871.JPG   Duckies Act 2.png

About how many ducks long is it?  Why did you choose that number?

There are 4 more cubes than ducks.

About how many cubes long is it?

Act 3:

IMG_4872.JPG

Were you correct?

If so, what were you thinking?

If not, what was your thinking?

3 Act Task: Lego Slide

Our 1st grade teachers are jumping into 3 Act tasks and asked me to find something that addressed non-standard measurement.  I made a couple of them that I will be posting. The standard addressed in Lego Slide is 1.MD.A.1 and it has students compare lengths of 3 objects.  See the nearpod here.

I was a little indecisive on which photos and videos to choose for this one, so I included all of them.  I chose to go with a fill in the blank comparison using vocabulary shortest and longest because this is what the data from our iReady assessment highlighted as a weakness for our students in first grade.  When I went to the unpacked standards for 1.MD.A.1 I saw an example of a logic type problem for this standard and really liked that. You may choose to go a different route.

Enjoy!  And as always, comments and suggestions are greatly appreciated!

Act 1:

Which box is longest?  Which is shortest?  Estimate.

Act 2:

Act 2 drawing pic

Which box is longest?  Which is shortest?  Prove how you know.

Fill in the blanks:

The white box is shorter than the blue box.

The yellow box is longer than the blue box.

The yellow box is longer than the white box.

The blue box is shorter than the yellow box.

Act 3:

all boxesall numberswhite blueyello whiteyellow blue

Were you correct?

Who is willing to share an incorrect solution?

Who is willing to share a correct solution?

What’s the math?

 

3 Act: Color Cubes

This task has 6 categories, but I think it is accessible to 2nd graders to address standard 2.MD.D.10.

Act 1:

What do you notice?  What do you wonder?

Estimate.  How many of each color cube are in the basket?

Act 2: 

act-2

There are 6 yellow cubes.  There are 2 more green cubes than yellow cubes.

There are the same number of orange cubes as red cubes.  There is one more orange cube than green cube.

There are the same number of blue and purple cubes.

There are 4 more purple cubes than Red cubes.

graph

Use the graph to to help you organize the data.

How many of each color cube are in the basket?

Act 3: 

Was your solution correct?

Who is willing to share a strategy for a correct solution?

Who is willing to share an incorrect solution?

What’s the math?

3 Act: What a Gem

One of our first grade teachers could not find a 3 act task for measurement or data analysis this week, so I made this data analysis task for 1.MD.C.4.  Here is a link to the Nearpod lesson.

Act 1:

What did you notice?  What do you wonder?

How many gems are in the box?  Estimate.

What do you know?  What do you need to know?

Act 2:

Act 2 JPEG

Graph.jpg

We decided to use this graph as an extra scaffold, but you could leave it out and have them draw their own bar graph.

Act 3: 

Was your solution correct?

What was the math you used?

I would love feedback on this one!  How can I make it better?