2.
GLE 36: Identify the domain and range of functions (P-1-H).
3.
GLE 37: Analyze real-life relationships that can be modeled by linear functions (P-1-H) (P-5-H).
4.
GLE 38: Identify and describe the characteristics of families of linear functions, with a
11.Make a list of how I have used math todayExamples:
-alarm clock with numbers
-money at McDonalds
-Bus driving 30 mph
14. If I were an inch tall15. If I were twelve inches tall16. What was my favorite part of todays lesson?
17. What was my least favorit
1.
GLE 34: Summarize information and relationships revealed by patterns or trends in a graph, and use the
information to make predictions (D-1-E).
2.
GLE 35: Find and interpret the meaning of mean, mode, and median of a small set of numbers (using
concret
HISTORICAL NOTE: Promulgated by the Board of Elementary and Secondary Education, LR 31:2843 (November 2005).
907.
A.
Benchmarks 9-12
Students in Grades 9-12 use number sense, estimation, models, drawings, manipulatives, and technology as
they extend their
3.
P-3-E: Recognizing the use of patterns, relations, and functions in other strands and in real-life
situations (2, 3, 4, 5).
NOTE:
The foundation skills addressed by each benchmark are listed numerically in parentheses after the benchmark.
AUTHORITY NOT
Mitchell D. Chester, Ed.D.
Commissioner of Elementary and Secondary Education
Massachusetts Curriculum Framework for Mathematics, March 2011
1
The 2011 Massachusetts Curriculum Framework for Mathematics is the result of the contributions of
many educators
Activity F: Observe formative assessment in action
Time needed: 15 minutes.
In this activity, you are provided with video extracts of Andrew, Dominic and Amy exploring how
formative assessment may be used to promote students learning. They are using the t
1.
GLE 24: Use mathematical terms to describe the basic properties of 3-dimensional objects (edges,
vertices, faces, base, etc.) (G-2-M).
2.
GLE 25: Relate polyhedra to their 2-dimensional shapes by drawing or sketching their faces (G-2-M)
(G-4-M).
3.
GLE
Handout 10: The effects of feedback on student learning
Mathematical Induction
Yue Kwok Choy
Question
Prove, by Mathematical Induction, that
n 1 2 n 2 2 n 3 2 . 2n 2 n 2n 1 7n 1
6
is true for all natural numbers n.
Discussion
Some readers may find it dif
"It's all very well telling us to assess our students, but how can
a busy teacher know what is going on inside 30 individual
heads?"
How would you answer this teacher?
What strategies do you have for finding out what
students are thinking in your lessons?
By the Principle of Mathematical Induction, P(n) is true for all natural numbers, n .
Question
Prove, by Mathematical Induction, that
1
1 n 2 n 1 3 n 2 . n 2 2 n 1 n n 1 n 2
6
is true for all natural numbers n.
Discussion
The "up and down" of the L.H.S.
4.
GLE 13: Switch between functions represented as tables, equations, graphs, and verbal representations,
with and without technology (A-3-M) (P-2-M) (A-4-M).
5.
GLE 14: Construct a table of x- and y-values satisfying a linear equation and construct a gra
Chapter 7.Strand Three: Measurement
701.
A.
Measurement
Focus. Measurement is the connection between numbers and the real word and as such is a vital component
of an attempt to organize the world. It allows one to communicate effectively and make decision
ACKNOWLEDGEMENTS
Joanna D. Krainski, Middle School Mathematics
Coordinator and Mathematics Teacher,
Tewksbury Public Schools
Raynold Lewis, Ph.D., Professor, Education
Chairperson, Worcester State University
Barbara Malkas, Deputy Superintendent of
School
10.
GLE 10: Calculate the value of a combination of bills and coins and make change up to $5.00 (N-6-E)
(M-1-E) (M-5-E).
11.
GLE 11: Add and subtract numbers of digits or less (N-6-E) (N-7-E).
12.
GLE 12: Round to the nearest 1000 and identify situations
Title 28, Part CXIX
Basic Factsaddition facts through 10 (0 + 0, 1 + 0, ,
10 + 10), subtraction facts which are the inverses of the
addition facts (20 10, , 1 0, 0 0), multiplication facts
(1 x 1, 1 x 2, , 10 x 10), and division facts which are the
Measur
Table of Contents
, which is divisible by 24 .
P(k + 1) is true.
By the Principle of Mathematical Induction, P(n) is true for all natural numbers, n .
Harder Problem :
Prove, by Mathematical Induction, that n(n + 1)(n + 2)(n + 3) (n + r 1) is divisible by
Activity E: Analyse students responses to concept-focused tasks
Minimum time needed: 20 minutes
On Handout 7, we present four mathematical topics and some sample student work on each one.
Ask participants to assess each response and try to identify the re
12.
GLE 12: Know the basic facts for addition and subtraction [0s, 1s, counting on and back 2s, doubles,
doubles + 1, then 10s fact, and related turn-around (commutative) pairs] and use them to solve real-life problems (N4-E) (N-6-E) (N-8-E).
13.
GLE 13:
Black, P., & Harrison, C. (2002). Working inside the black box:
Assessment for learning in the classroom. King's College
London School of Education.
Now published by GL Assessment:
http:/shop.gl-assessment.co.uk
In this booklet, the authors describe a pro
Activity B: Teachers' own experiences of formative assessment
Minimum time needed: 10 minutes.
What do teachers know about their students and what consequential action do they take?
Ask participants to work in pairs, considering the following questions.
T
Building on what students already know
How can I respond to students in ways that improve their learning?
Introduction
Inquiry-based teaching assumes that students do not arrive at sessions as blank slates, but as actively
thinking people with a wide vari
The Standards for
Mathematical Content
PRE-KINDERGARTENGRADE 8
Organization of the Pre-Kindergarten to Grade 8 Content Standards
The pre-kindergarten through grade 8 content standards in this framework are organized by grade level.
Within each grade level
The pattern of activities on handout 9 is as follows:
Handout 9: A formative
Give the problem before the lesson and ask students to attempt it.
assessment lesson plan
(20 minutes)
Collect in the work and prepare some constructive, qualitative
feedback.
In
Grade 3
Overview
Operations and Algebraic Thinking
and estimation of intervals of time,
Represent and solve problems involving
liquid volumes, and masses of objects.
multiplication and division.
Solve problems involving measurement
Understand properties o
Directions: Take an 8x11 piece of paper or construction paper. Split your paper into fourths, as shown
below:
Label each box with one of the properties we learned today. Then, you are to demonstrate what that
property looks like using pictures. See the ex
Activity D: Analyse students responses to problem-solving tasks
Minimum time needed: 20 minutes
Handout 4 presents three problems together with four student responses on each. The tasks are: Counting
Trees, Cats and Kittens, Security Cameras.
Read through
17. If I had a magic wand in math class, what would I use it on?
18. If I were invisible, how would I help the class in math?
19. Invent a new shape-name it, draw it, and tell how it is used.
20. The most important part of solving a problem is.
21. If mat
Date:
Class:
Commutation Property: Change Order The order doesnt matter; you will get the same answer.
Commutative of Addition: 4 + 5 = 5+4
Commutative of Multiplication: (6)(7) = (7)(6)
Associative Property: Grouping Changes The parenthesis will move but
Chapter 19
Open book management
- Decentralized philosophy
- Get every employee thinking like an owner
- Information sharing and teamwork
- Allows employees to see the financial condition of company
- See how his/her job fits into organizational success
T