5th Step, a Mathematical Exploration: What is a Brain?
Guiding Question:
What is a brain?
Time Suggested:
80+ minutes
Overview: In this Step, learners will draw what they imagine their brains to look like inside their heads.
As a class, everyone will listen to one text, then independently read (or re-read) one or more of the three
leveled informational texts about the brain, using the annotation skills they developed in the 3rd and 4th
Steps. Finally, using what they’ve learned from the text and their understanding of area and fractions,
they’ll draw a mathematically proportional brain inside a new tracing of their heads.
Standards Addressed in Step 5:
NGSS 4-LS1-1 Construct an argument that plants and animals have internal and external structures
that function to support survival, growth, behavior, and reproduction. [Assessment
Boundary: Assessment is limited to macroscopic structures within plant and animal
systems.]
NGSS 4-LS1-2 Use a model to describe that animals receive different types of information through
their senses, process the information in their brain, and respond to the information in
different ways. [Assessment Boundary: Assessment does not include the mechanisms
by which the brain stores and recalls information or the mechanisms of how sensory
receptors function.]
CCSS.ELA-LITERACY.RF.4.3.A Use combined knowledge of all letter-sound correspondences, syllabication patterns,
and morphology (e.g., roots and affixes) to read accurately unfamiliar multisyllabic
words in context and out of context.
CCSS.ELA-LITERACY.RF.4.4 Read with sufficient accuracy and fluency to support comprehension.
CCSS.ELA-LITERACY.RI.4.1 Refer to details and examples in a text when explaining what the text says explicitly
and when drawing inferences from the text.
CCSS.ELA-LITERACY.RI.4.2 Determine the main idea of a text and explain how it is supported by key details;
summarize the text.
CCSS.ELA-LITERACY.RI.4.4 Determine the meaning of general academic and domain-specific words or phrases in
a text relevant to a grade 4 topic or subject area.
CCSS.ELA-LITERACY.W.4.7 Conduct short research projects that build knowledge through investigation of different aspects of a topic.
CCSS.ELA-LITERACY.W.4.2.D Use precise language and domain-specific vocabulary to inform about or explain the topic.
CCSS.ELA-LITERACY.SL.4.1.A Come to discussions prepared, having read or studied required material; explicitly
draw on that preparation and other information known about the topic to explore
ideas under discussion.
CCSS.MATH.CONTENT.4.NF.A.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual
fraction models, with attention to how the number and size of the parts differ even
though the two fractions themselves are the same size. Use this principle to recognize
and generate equivalent fractions.
CCSS.MATH.CONTENT.4.MD.A.2 Use the four operations to solve word problems involving distances, intervals of time,
liquid volumes, masses of objects, and money, including problems involving simple
fractions or decimals, and problems that require expressing measurements given in a
larger unit in terms of a smaller unit. Represent measurement quantities using
diagrams such as number line diagrams that feature a measurement scale.
CCSS.MATH.CONTENT.4.MD.A.3 Apply the area and perimeter formulas for rectangles in real world and mathematical
problems.
CCSS.MATH.PRACTICE.MP4 Model with mathematics.
CCSS.MATH.PRACTICE.MP7 Look for and make use of structure
Evidence: How will learners demonstrate understanding?
Learners will apply what they’ve learned about their brains to create a two-dimensional drawing of
their brains on grid paper that takes up 2 3 of the area inside their head tracings.
Materials Needed:
Plant Growth Measuring Charts (learners should have these in their science notebooks/folders)
“What is a brain?” informational texts (provide each learner with all four levels)
Audio versions of each text (optional)
“How to Annotate” Chart Paper (from the 3rd step)
Grid paper handout (two for each learner) p. 44
Teacher’s Guide to Step 5
1. Use the Plant Growth Measuring Charts to check in on the seeds that were planted in the 2nd Step.
Celebrate careful observations of growth, stunted or no growth, and death, always encouraging learners to
continue tending their plants according to the model they constructed. Have learners calculate the change
in height of their plants, comparing new measurments to previous ones (a chance to practice subtracting
mixed numbers & simple fractions).
2. Visit The River with the class. Remind them of the Essential Question and ask if anyone (including
you!) has gathered any evidence so that some of the Think We Know and Wonder sticky notes can flow
into the Sea of Discovery. The class decides whether the evidence presented is viable before celebrating a
sticky note flowing into the Sea of Discovery.
3. Now add the next Guiding Question to The Cloud: What is a brain?
a. Allow time for you and your learners to generate new questions and prior knowledge about the
new guiding question. Use sticky notes to keep The River flowing.
4. “Have you ever wondered what your brain looks like inside your head?” Invite learners to trace
outlines of the top half of their heads (down to about the tip of their noses and down past the bump on
the backs of their heads) on the special grid paper provided on page 44. Each learner will match their left
ear to the ear drawing on the grid paper. Encourage learners to be careful to avoid angling their pencils
inward, thereby drawing head outlines much smaller than their actual heads. Asking help from a friend
may be useful as well.
5. Next, they should draw what they think their brain looks like inside their head outline. Give some time
for learners to share their brain drawings, and to share where they got the ideas to draw the way they did
(e.g., heard someone describe it once, saw a movie that had a brain in it, etc.)
6. “So these *might* be what our brains look like… but what IS a brain exactly?”
7. Pass out the packet of “What is a brain?” texts (p. 45 -52), and read through Variation 1 (lowest reading level) out loud while everyone follows along together. Invite discussion: “What was surprising?
Confusing? Did anyone visualize anything while reading?”
8. Remind them of the annotation skills they started developing in the 3rd Step. Have learners read
through the text again, annotating as they go and then provide some time for learners to share their
annotations: “What did you draw? What questions came up for you?”
9. “The next two “What is a brain?”
texts have the same basic information
but explore the ideas in more depth read both (or one) and annotate it as
well, seeing what new information
you’re able to learn from these deeper
texts.”
10. After a while, give learners a chance to
share additional learning and questions
that arose for them. Make sure to encourage them to add these to The River.
11. “Now that we have a better
undertanding of what a brain is, let’s
draw our brains again, but this time
let’s use what we just learned and
what we know about fractions and
area to be more accurate.”
12. First, ask learners to find their nasion and inion. The nasion is another word for the top of the bridge
of the nose, between the eyes, where the nose curves toward the base of the forehead. The inion is the
prominent bump you can feel at the center-back of your skull. The curve of the skull changes abruptly
inward as the skin slopes to join the neck. Locate the nasion and inion with all learners and remind them
that their brain fills most of the inside of the skull above that plane.
13. Instruct learners to trace their head again on the sample graph paper, and then using a ruler, draw a
line on their head tracing that connects the nasion to a point two finger-widths below the inion as shown
in the example (Bryan’s Head, p. 41).
14. “Now that we’ve learned that this is the area within our heads where our brain lives, and
that the brain takes up about 2 3 of this space, how can we draw our brains in the space in a
way that’s mathematically accurate?” Before anyone begins this task, send learners off in groups to
brainstorm strategies, and then invite learners to share strategies with the class.
15. “Now that we’ve heard some strategies that could help us use math to draw our brains
more accurately, try again to draw your brain inside the outline of your head on grid paper, but
this time, make sure that it takes up exactly 2 3 of the space. Include words, numbers, and
labels to explain your thinking on the grid paper.”
16. Walk around while learners are working, encouraging them to come up with mathematical reasons for
the choices they make in their drawings (e.g., What strategy are you using to make sure your brain drawing is using 2 3 of the area inside your skull? How can you be sure? Why are you using those shapes,
colors, and features in your model of your brain?)
17. Have learners reflect on the evolution of their understanding about their brains by comparing the two
drawings they have made in this Step.
On the next page are three examples from 4th grade learners
completing their head tracings and calculating the area of their
skulls and brains
A learner has thoroughly counted and
numbered all full and partial squares
inside the head to calculate the total
area between the nasion and
two-finger’s distance below the inion.
A learner carefully colors 2/3 of
the counted and numbered
space. inside the skull tracing.
A better understanding of brain
dimensions achieved through
mathematics!
1 cm
1 cm
What is a brain? by Bryan, Paul, and Sara
Variation 1
Your body is alive because it has many parts working together. There is a lot
inside your body that you cannot see, including your brain. Your brain is a
living organ that fills about two-thirds of your head above your ears. While
larger humans usually have larger brains, a larger brain is not always a
smarter brain.
Your brain is pink, soft, mushy, wobbly, and sits in cushiony liquid inside
your skull because it is very, very fragile. Your hard skull and fast reflexes
help to naturally protect your brain... but your brain also needs your
attention and careful care to be healthy.
You use one hundred percent of your brain every day. Use your mind and
brain all the time to discover how you, along with your brain, can thrive.
Does your food diet give your brain all the nutrients it needs? Are you
sleeping, running around, and playing enough? Are you choosing to put
healthy information with the right amounts of energy into your senses?
Your brain helps you understand what you sense from your ears, eyes,
tongue, nose, skin, and muscles. You use it to listen, talk, move, and learn
just about anything. Like a muscle, your brain becomes stronger when you
pay attention to what you do. What activities and ways of thinking do you
want to become really strong at?
Glossary:
Alive (adjective) - Describes living things that survive by keeping healthy.
a·live [uh-lahyv]
Attention (noun)- The skill you have to focus and avoid distraction.
Listening carefully is one way you can show others you are paying attention.
at·ten·tion [uh-ten-shuh n]
Focus (noun)- To pay attention to; to concentrate on.
fo·cus [foh-kuh s]
Fragile (adjective)- Like a bubble, some things, like your brain, can break.
Fragile is another word for delicate. You should be very gentle and take care
of things that are fragile, especially your brain!
frag·ile [fraj-uh l]
Head (noun)- The top part of your body that has many of your senses on
the outside and contains your brain on the inside.
head [hed]
Organs (noun) - Parts of the body, made of cells and living tissue, that work
together for the purpose of survival.
or·gans [awr-guhs n]
Senses (noun) - The parts of your body that help you detect and connect
with the world outside of your body.
senses [sens-iz]
Skull (noun) - The hard bone that is just under the skin of your head. Your
brain is inside of your skull.
skull [skuhl]
What is a brain? by Paul, Sara, and Bryan
Variation 2
Your body is made of millions of small, living cells and many liters of fluid
working together. Two special kinds of cells that live in your body are called
neurons and glia. While you communicate with your friends using words and
gestures, neurons and glia inside your body communicate using chemicals
and electricity! There are about 86 billion (86,000,000,000) neurons and
thousands of millions of glia in your head! This huge collection of cells is a
very important organ, and you use one hundred percent of it every day. Can
you guess what it is?
If you were able to look inside your head, your brain would probably look
wrinkly, pink, and feel soft. Inside the protective, hard skull, your extremely
fragile brain is surrounded by a fluid that cushions it from impact and helps
nutrients flow to keep it healthy. If you took your living brain out of your
skull and put it on a table, it would bobble like gloppy brain pudding. Don't
do this, because you would no longer stay living! To feel where your brain
lives inside your skull, using both hands, trace a line from the curve between
your eyes (just above your nose, along your eyebrows), back around your
ears, to the back of your head. Then go over the top of your skull back to
where you began. Did you know your amazing brain fills about two-thirds of
this portion of your head!? In history, people thought that bigger brains are
smarter brains, but scientists now know it’s much more complicated than
that.
Your brain changes all the time. The communication between neurons
changes while you are learning, focusing, playing, and sleeping. This
communication becomes strong when you use it. Let's imagine you are
trying to memorize math facts. The connections between neurons are weak
the first time you try to remember that 7 X 9 = ______. But these
connections get stronger and faster when you practice with focus. As a
metaphor, you might say that the neurons send messages to each other
over a mountain trail. When you practice, the trail gets strong and clear.
5 X 3 = _______
5 X10 = _______
You are becoming faster with your math facts.
But what happens if you don't practice math facts for a long time? It's like
the trail is no longer being walked on. The trail starts to fade, so your
memory of 7 X 9 = ______ will begin to fade along with it. This is interesting
indeed! It means you can choose the connections you strengthen or weaken
by deciding to focus your brain on some things and not others. How can you
choose wisely?
Glossary:
Cells (noun) - The smallest living parts of a body.
cell [sel]
Chemicals (noun) - Very small building blocks of life that have a specific
size and shape.
chem·i·cals [kem-i-kuh ls]
Communication (noun) - Successfully sharing ideas and feelings with
another.
com·mu·ni·ca·tion [kuh-myoo-ni-key-shuh n]
Delicate (adjective) - Easily broken or damaged.
del·i·cate [del-i-kit]
Focus (verb) - To pay attention to; to concentrate on.
fo·cus [foh-kuh s]
Gestures (noun) - Actions that show thoughts, feelings, or intentions.
ges·ture [jes-cher]
Glia (noun) - A type of cell in the brain and spinal cord that works with
neurons to support brain functioning.
gli·a [glee-uh]
Impact (noun) - Two objects hitting each other with a lot of force.
im·pact [im-pakt]
Fluid (noun) - Flowing stuff that can easily change its shape.
flu·id [floo-id]
Metaphor (noun) - Describing one thing to help understand another similar
thing.
met·a·phor [met-uh-fawr]
Neurons (noun) - Cells that live in, and make up, much of the brain.
neu·rons [noo r-ons, nyoo r-]
Nutrients (noun) - Chemicals that a body needs to live and grow.
nu·tri·ents [noo-tree-uh nts, nyoo-]
Skull (noun) - The bones of the head that surround the brain.
skull [skuhl]
Wise (adjective) - Having or showing the power and intelligence to judge
what is true.
wise [wahyz]
What is a brain? by Sara, Bryan, and Paul
Variation 3
Your body is a collection of tens of trillions of cells and many liters of fluid
working together. Every cell is biotic; it is the smallest living building block
of your body. About ½ of one percent of all your cells are called neurons and
glia. Neurons and glia communicate throughout the body using chemicals
and electricity. A collection of about 86 billion neurons and many billions of
glia form a very important organ inside of your head. Can you guess what
this organ is called?
Protected inside the skull, your very fragile brain is surrounded by
cerebrospinal fluid that cushions it from impact during movement and helps
nutrients flow. If you were able to look inside your head, your brain would
probably look wrinkly, pink, and feel soft. Neurons and glia are almost
transparent, but there are a lot of red blood vessels in your head, too (which
is why your brain looks pink). If you took your living brain out of your skull
and put it on a table, it would wobble-bobble like gloppy brain pudding.
Don't do this though, because you would no longer stay living! While the
brain is amazing, it needs very special care from you.
To feel where your brain lives inside your skull, using both hands, trace a
line from the curve between your eyes (just above your nose), along your
eyebrows, back around your ears, to the back of your head. Then go over
the top of your skull back to where you began. Your brain takes up about
two-thirds of this space inside of your skull. There have been times in
history when people have used brain size (and even head size!) to claim that
certain people are more intelligent than others. While larger humans usually
have larger brains, intelligence does not necessarily depend upon brain size.
Intelligence is a talent you develop.
The neurons and glia within your brain adapt all the time to the choices you
make. Don’t be fooled by any myths you may have heard, you use one
hundred percent of your brain every day. The communication between
neurons, glia, and other cells of the body change while you are learning,
focusing, playing, and sleeping. This communication becomes stronger with
use. Let’s say you were trying to understand fraction equivalence. At first,
the connections between neurons that help you understand that
1
2
is the
same as 0.5, ____, 50%, or "half" are new and weak, but, with focused
practice over time they become stronger and quicker. As a metaphor, you
might say that the neurons send messages to each other over a mountain
trail. When you practice, the trail gets strong and clear and you become
more confident with math concepts like these.
What happens if you don’t use these math concepts for a long time? It’s like
the trail is no longer being walked on; neurons are not communicating with
one another about math. The trail that connects them starts to fade, so your
understanding that
1
2
is the same as 0.5, ____, 50%, or "half" will begin to
fade, too. This is interesting indeed! It means you can choose the
connections you strengthen or weaken by deciding to focus your brain on
some things and not others. How can you choose wisely?
Glossary:
Below, write the words you didn't understand and find out what they mean
before you read again.
What is a brain? by You and…
Variation 4