A Way to Make Math Make Sense
NMSA 2011
Linda Bridges and Jeanne Simpson
Virtual handout at jeannesimpson.wikispaces.com
 Sometimes
teachers have to
explain “why”
mathematical
concepts are true.
Why can’t you
divide by
zero?
Why should we
write in math
class?
According to Marilyn Burns there are two major
benefits:
 It supports students’ learning by helping them
organize, clarify, and reflect on their thinking.
 It benefits teachers because students’ papers are
invaluable assessment resources.
Instructor Magazine, April 1995
1.
2.
3.
4.
5.
Write arguments focused on discipline-specific
content.
Write informative/explanatory texts, including the
narration of …scientific procedures/experiments, or
technical processes.
Write narratives to develop real or imagined
experiences…
Produce clear and coherent writing…
…develop and strengthen writing…by planning,
revising, editing, rewriting,…
Use technology, including the Internet, to produce
and publish writing and present the relationships
between information and ideas…
7. Conduct short research projects to answer a
question…
8. Gather relevant information from multiple … sources
9. Draw evidence from informational texts to support
analysis, reflection, and research.
6.
10. Write routinely over extended time
frames (time for reflection and
revision) and shorter time frames (a
single sitting or a day or two) for range
of discipline specific tasks, purposes,
and audiences.
Construct viable arguments and
critique the reasoning of others.
Attend to precision.
 6.NS.4. Find the greatest
common factor of two whole
numbers less than or equal to 100
and the least common multiple
of two whole numbers less than
or equal to 12. Use the
distributive property to express a
sum of two whole numbers 1–100
with a common factor as a
multiple of a sum of two whole
numbers with no common
factor. For example, express 36 +
8 as 4 (9 + 2). Apply and extend
previous understandings of
numbers to the system of rational
numbers.
Factor
Product
Multiple
Divisibility
12
18
30
45
Explain a way to
determine the greatest
common factor of any
pair of numbers.
 6.RP.3. Use ratio and rate reasoning to solve real-world and
mathematical problems, e.g., by reasoning about tables of
equivalent ratios, tape diagrams, double number line
diagrams, or equations.
 Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity
means 30/100 times the quantity); solve problems involving finding
the whole, given a part and the percent.
 7.RP.3. Use proportional relationships to solve multistep
ratio and percent problems. Examples: simple interest, tax,
markups and markdowns, gratuities and commissions,
fees, percent increase and decrease, percent error.
 7.SP.8. Find probabilities
of compound events
using organized lists,
tables, tree diagrams, and
simulation. Understand
that, just as with simple
events, the probability of
a compound event is the
fraction of outcomes in
the sample space for
which the compound
event occurs.
 Analyze outcomes when rolling one and two dot cubes
 “Describe the probability of rolling a sum of 7 in words
and in fractions with lowest terms.”
 Conduct experiments with rolling two dot cubes
 “Describe the results of your experiment. Compare the
results with the theoretical probability of rolling a 2 one
time out of every 6 rolls.”
 “What do you think about the theory of large numbers?”
 Design an experiment
 “Describe the results of your experiment.”
 Analyze combinations using lists and tree diagrams
 “In what ways do the lists, tree diagrams, and
multiplication compare? Which representation is your
first choice? Explain.”
How can this
work in my
classroom?
Things I learned
Things that surprised me
Question I still have
Virtual handout at jeannesimpson.wikispaces.com