WEBVTT

00:00:00.046 --> 00:00:06.976
[Music] Welcome to Helping 
All Students Learn Algebra.

00:00:08.166 --> 00:00:11.246
Hi, I'm Paul Jorgens, and I'm 
an eighth grade math teacher

00:00:11.246 --> 00:00:13.396
at Terman Middle School
in Palo Alto, California.

00:00:13.956 --> 00:00:15.956
I teach three sections of algebra.

00:00:17.156 --> 00:00:22.316
The students in the Introductory 
Algebra course have some areas of math

00:00:22.316 --> 00:00:26.696
that they're still working on and 
so, as we teach the algebra standards,

00:00:26.786 --> 00:00:29.226
we need to be building their 
skills with integers,

00:00:29.226 --> 00:00:32.625
their skills with fractions, 
graphing, problem-solving,

00:00:33.206 --> 00:00:36.436
and we do that concurrent
with teaching the algebra standards.

00:00:37.196 --> 00:00:39.286
At the end of the year, we'll 
test all of our students

00:00:39.286 --> 00:00:42.936
on the algebra standards,
and with the goal

00:00:42.936 --> 00:00:47.396
that they will all be successful
and knowing that we'll have moved all

00:00:47.396 --> 00:00:49.036
the Introduction to Algebra 
students forward

00:00:49.036 --> 00:00:50.566
and that many of them will
be successful.

00:00:50.766 --> 00:00:56.016
So in the Introduction to Algebra class,
what we found is that we need to--

00:00:56.286 --> 00:01:01.156
for instance, when we do equations,
the students start solving equations

00:01:01.156 --> 00:01:03.136
where all the answers 
are whole numbers.

00:01:03.236 --> 00:01:05.846
And so we might start
with multi-step equations,

00:01:05.846 --> 00:01:07.516
but we will start with 
whole numbers.

00:01:07.556 --> 00:01:09.886
And then we will bring
in the negative numbers,

00:01:09.886 --> 00:01:11.046
and then we will bring 
in the fractions

00:01:11.046 --> 00:01:14.056
after that, so they have the skill
of the equations first.

00:01:14.056 --> 00:01:16.356
And then we can work on their 
skills with integers,

00:01:16.356 --> 00:01:18.356
their skills with 
fractions to follow.

00:01:18.986 --> 00:01:21.216
If I don't do that, 
I can't diagnose,

00:01:21.216 --> 00:01:23.206
"Well, where is the struggle
with inequalities?

00:01:23.206 --> 00:01:24.476
They are not getting the right answer."

00:01:25.076 --> 00:01:28.676
And they are not getting good 
feedback about where their struggle is.

00:01:28.756 --> 00:01:31.346
And so I have learned that, 
instead of starting

00:01:31.346 --> 00:01:34.166
with small inequalities
and then making them more messy

00:01:34.166 --> 00:01:38.466
or complex, it is better to start
with kind of multi-step inequalities

00:01:38.786 --> 00:01:42.376
but then start with results
that are whole numbers and build

00:01:42.376 --> 00:01:44.316
in the negatives and the 
fractions later.

00:01:44.696 --> 00:01:48.626
So in this lesson, my goal was 
for students to communicate

00:01:48.626 --> 00:01:52.146
with each other about graphs
and about graphs as they relate

00:01:52.146 --> 00:01:54.926
to tables, equations, and words.

00:01:54.926 --> 00:01:58.586
I think that's really important
at learning algebra at any

00:01:58.586 --> 00:02:03.746
of the levels is that we have
to utilize not only students' ability

00:02:03.746 --> 00:02:07.666
to write algebraically,
but they need to really speak

00:02:07.916 --> 00:02:10.996
algebraically and develop
that language of algebra.

00:02:11.586 --> 00:02:15.066
Coming into this lesson they had 
done some work with patterns.

00:02:15.416 --> 00:02:18.186
They could see a pattern,
a consistent pattern in the table

00:02:18.186 --> 00:02:21.446
where there was a constant rate
of change, that that would form a line

00:02:21.446 --> 00:02:22.516
when they graphed it.

00:02:22.556 --> 00:02:27.726
And so they had some vocabulary related
to lines, like intercept or slope.

00:02:28.006 --> 00:02:31.666
They know the word quadrant,
and so some of the vocabulary that goes

00:02:31.666 --> 00:02:35.216
with coordinate plane was necessary
for them to be able to communicate

00:02:35.216 --> 00:02:36.356
with the other student.

00:02:36.356 --> 00:02:42.556
One piece of the lesson was for students
to have all of these cards with tables,

00:02:42.556 --> 00:02:46.886
graphs, equations, and words,
and then they had to sort them together

00:02:46.886 --> 00:02:49.966
and match them so the table
and the graph and the equations

00:02:49.966 --> 00:02:53.646
and the words went together
as a function family.

00:02:54.196 --> 00:02:57.286
I gave each group 24 cards.

00:02:57.286 --> 00:03:03.446
They had six equations, six graphs, 
six sets of words that matched a graph,

00:03:03.516 --> 00:03:05.696
and six tables.

00:03:05.696 --> 00:03:10.216
And so what I found was I needed
to sometimes guide them because 24 cards

00:03:10.216 --> 00:03:12.426
on their table is a little bit 
too much information.

00:03:12.836 --> 00:03:14.646
And so sometimes,
I would need a guide them

00:03:14.646 --> 00:03:18.666
by asking them questions like, "Well,
can you find the y intercept?

00:03:18.666 --> 00:03:20.586
Can you match up the intercepts,
or can you match

00:03:20.586 --> 00:03:22.666
up the pattern you are seeing?"

00:03:22.666 --> 00:03:28.866
In the end, all of the groups were 
successful at matching the four.

00:03:28.936 --> 00:03:33.376
We follow that with them back-to-back
describing graphs to each other;

00:03:33.376 --> 00:03:37.136
one person seeing the graph, and 
one person drawing what was described.

00:03:37.136 --> 00:03:41.416
One student would be viewing a graph
or a series of graphs on the screen

00:03:41.726 --> 00:03:45.016
and needing to describe
to the student facing away

00:03:45.016 --> 00:03:46.406
from the screen what 
they were seeing.

00:03:46.836 --> 00:03:51.856
And so they were using vocabulary
like steep or slant or intercept

00:03:51.856 --> 00:03:54.966
or parallel, all kinds of vocabulary
that they had been picking up,

00:03:54.966 --> 00:03:57.466
now they were needing it 
to describe it

00:03:57.756 --> 00:04:00.576
to the person that couldn't see
the picture.

00:04:00.776 --> 00:04:05.006
Students struggled more with 
seeing the graph to match the table

00:04:05.346 --> 00:04:10.796
than I expected, and so I needed 
to follow that up with some more work

00:04:10.796 --> 00:04:14.286
with tables and graphs
and matching them together

00:04:14.496 --> 00:04:16.776
and building a graph 
from a table.

00:04:16.776 --> 00:04:19.886
And then I found that if 
I gave them a graph

00:04:20.125 --> 00:04:23.756
and they could build tables from that,
that they were starting to understand

00:04:23.756 --> 00:04:26.346
that this graph was this 
infinite set of points.

00:04:26.766 --> 00:04:30.566
We need to work from graphing 
from a lot of different angles with them,

00:04:31.006 --> 00:04:34.006
so that they're talking about 
it with other students,

00:04:34.116 --> 00:04:38.506
they are graphing it by points,
they are graphing it by pattern.

00:04:39.116 --> 00:04:41.156
That's the skill that 
is really one

00:04:41.156 --> 00:04:43.106
of the most difficult to develop
with eighth graders.

00:04:43.526 --> 00:04:47.056
We are going to use the equation solving
skills that they have acquired

00:04:47.056 --> 00:04:50.756
previously, so now when they look
at an intercept, they can figure

00:04:50.756 --> 00:04:54.566
out it algebraically rather
than by looking at the table

00:04:54.566 --> 00:04:57.406
or by looking at the graph and 
trying to eyeball the intercept.

00:04:57.446 --> 00:05:00.836
So they have got this concept
of what intercept is, but now we need

00:05:00.836 --> 00:05:03.606
to use their equation-solving 
skills to take the next step.

00:05:04.616 --> 00:05:08.686
The closure was really also the 
preview for next week,

00:05:08.686 --> 00:05:13.316
telling them how they're going to 
use some of the vocabulary and skills

00:05:13.426 --> 00:05:17.086
that they were working with in 
graphs, equations, and tables,

00:05:17.126 --> 00:05:19.056
and where we are going next week.

00:05:19.056 --> 00:05:23.226
And so I presented problem called
co-linear trio that they would be seeing

00:05:23.226 --> 00:05:27.186
and told them how what we had done 
not only in that lesson,

00:05:27.186 --> 00:05:30.706
but in the few lessons leading up to it,
were going to help us be successful

00:05:30.706 --> 00:05:32.336
for where we are going next week.

00:05:32.336 --> 00:05:35.976
One of the things that I found in 
the Introductory Algebra course is a

00:05:35.976 --> 00:05:39.126
lot of times all of a sudden 
students will start getting

00:05:39.126 --> 00:05:41.926
it and really making fast progress.

00:05:42.086 --> 00:05:47.436
And so, I have to build in opportunities
for them to join the other group of kids

00:05:47.626 --> 00:05:48.926
in ninth grade.

00:05:48.926 --> 00:05:52.566
And so differentiating by sometimes 
giving them different homework problems

00:05:52.616 --> 00:05:55.986
or sometimes asking them 
to do a little bit further

00:05:56.306 --> 00:05:59.866
in a problem-solving context
so that they can have that chance

00:05:59.866 --> 00:06:02.726
because at some point,
for some of the students,

00:06:02.726 --> 00:06:04.236
it's going to become easy for them.

00:06:04.646 --> 00:06:07.976
And they can have
that opportunity to move up.

00:06:08.046 --> 00:06:11.546
To learn more about Helping All 
Students Learn Algebra,

00:06:11.546 --> 00:06:15.486
please explore the additional resources
on the Doing What Works website.