Day by day list of course topics:
date topics discussed resources Monday, August 19 factors, multiples and hands-on problems for these
concepts Section 6.1 in text Class activities 6A, 6B, 6C Wednesday, August 21 greatest common factors, least common multiples, and
hands-on problems for these concepts; fraction addition and subtraction: explaining why we need
a common denominator; story problems for fraction addition
and subtraction, story problems for fraction subtraction
problems that seem like they correspond to the fraction
subtraction problem but actually don't Section 6.3 in text Handout class activity on adding fractions. Monday, August 26 Playing with pattern tiles leads us to deeper mathematics
than we might expect: when we fill shapes with pattern tiles
we discover that in some shapes we can't use the
orange squares and the white thin rhombuses to fill the
shape, whereas in other shapes we must use either the
orange squares or the thin white rhombuses (or both) to fill
the shape. This is a physical manifestation of the
mathematical fact that the square root of 3 is not a
rational number, i.e., cannot be expressed as a fraction of
whole numbers. fractions: adding fractions and the lcm of the
denominators; examination of Saxon materials on fractions;
the need to be aware of the whole associated to a
fraction Sections 6.3 and 6.4 in text. Class activity 6K Class activity 6H Handout class activity on adding fractions. Copies of Saxon materials. Wednesday, August 28 Equivalent fractions, as taught in the textbooks used in
Singapore. Fraction multiplication: making story problems for
fraction multiplication problems. Using pictures to solve a
fraction multiplication problem. We examined five fraction
multiplication teaching episodes from an article by Nancy
Mack. We looked at how the sequence of problems were
designed to build students' knowledge. We discussed how the
teacher prompted students in their thinking. Copies from texts used in Singapore. Copies of excerpts of an article on fraction
multiplication by Nancy Mack. Text, section 4.9 Wednesday, September 4 Different ways to solve mixed number subtraction problems
such as 3 1/2 - 1 3/4. Fraction multiplication in the Singapore text: they first
learn about a fraction times a whole number, then they do
applications of this such as the number of minutes in 3/4 of
an hour. Then they do fraction times fraction, showing a
relevant picture next to each problem. Fraction division: the two ways to interpret division and
story problems for both interpretations. We agreed that the
"how many groups?" (measurement) interpretation is easier to
grasp when it comes to fraction division. Using pictures to
solve fraction division problems and to see how "invert and
multiply" comes about. Fraction division in Singapore text:
fraction divided by a whole number. Copies of portions of text used in Singapore, grade 5,
for fraction multiplication and division. Text, section 5.5, class activity 5K Monday, September 9 How to teach a visually impaired student about fraction
multiplication? What do we need to understand in order to be able to make
sense of fraction division? As with fraction multiplication,
we need to be able to work with different wholes. We need to
be able to treat something made up of several parts as a
whole in its own right. Fractions and division, writing a fraction as a decimal:
activities 5G, 5H. Text, sections 5.3, 5.5, activities 5G, 5H, and 5K. Wednesday, September 11 Different ways to explain why we place the decimal point
where we do in decimal multiplication problems: 1) using
graph paper (or base-ten blocks or unifix cubes). 2) By
writing the decimals as mixed numbers and using fraction
multiplication. 3) By thinking about the sizes of the
numbers and thereby realizing there is only one reasonable
location for the decimal point. Multiplying mixed numbers: this is similar to multiplying
decimals. How many marshmallows in marshmallow structures? How many
curlicues? How many dots? How many gumdrops? How many
hearts? How many stars? volume 1 activities, pages 97, 98,
103, 108, 109. Different ways of writing expressions for
"how many": pre-pre-pre algebra. Text, section 4.11, activity 4EE. Text, section 4.6. Monday, September 16 Algebra: how many small shapes in a growing pattern of
shapes? Equations that correspond to multi-colored designs.
Equations that correspond to sequences of multi-colored
designs. Text, section 10.1, activities 10A - 10D. Wednesday, September 18 Algebra: given a sequence of numbers, create a
corresponding sequence of pictures. Algebra activities from
Navigating through Algebra in Grades PreK - 2 and
Grades 3 - 5 by NCTM. Activities involving repeating
patterns. Copies from Navigating through Algebra in Grades
PreK - 2 and Grades 3 - 5 by NCTM Text, section 10.1, activities 10B, 10H, 10I Monday, October 28 Discussion of math in the field Wednesday, October 30 Functions: ways of representing functions (formula,
table, graph); not all functions have a formula;
interpreting graphs of functions; stories to go along with a
graph; which stories have you seen for which you could draw
a corresponding graph? Text, section 10.2, activity 10K Monday, November 4 Statistics: conducting surveys, representative samples,
setting up experiments Text, section 11.1, activities 11A, 11B, 11C Wednesday, November 6 Common data displays: real graphs, pictographs, bar
graphs, double bar graphs, line plots, line graphs, pie
charts Text, section 11.2, activities 11D, 11E, 1 and 2. Monday, November 11 Three levels of questions about graphs. Misleading data
displays. The average as "making even" or "leveling
out". Text, section 11.2, activities 11F, 11G. Text, section
11.3, activity 11J Wednesday, November 13 Average as "balance point". Average versus median: ways
to get the same average but different medians (by
rearranging block towers), ways to get the same median but
different average by "shifting the balance point". Text, section 11.3, activities 11K, 11L, 11M Monday, November 18 Can 90% be above average? M&M activity. Spread of
data: percentiles. Text, section 11.3, 11.4, activities 11N, 11O Wednesday, November 20 Percentiles vesus percent correct. How percentiles inform
about the spread of data. Standardized testing. activities 11O, 11P, example of Standford-9 printout,
article: Explaining
Test Results to Parents see also: Norm
and Criterion Referenced Testing and Common
Misuses of Tests Monday, November 25 Probability text and class activities, section 12.1 Monday, December 2 Probability text and class activities, section 12.1 Wednesday, December 4