2007 Mississippi Department of Education 2007 Mississippi Mathematics Framework Training Revised (Grades K-5) Day 2

2007 Mississippi Department of Education

2007 Mississippi Mathematics Framework Training Revised (Grades K-5)

Day 2


Reading Reflections

At your table, discuss important ideas you took from the articles you read.

How did the ideas relate to our tasks and discussions from yesterday?

How did the ideas relate to our exploration of the curriculum framework?

Record your ideas on chart paper.


Understanding by Design: Step 1

1. Define desired results a. Establish goals: What relevant goals (such as content,

competencies, or objectives) will this design address? b. Understandings: What are the big ideas that students will

understand? What specific understandings about them are desired? What misunderstandings are predictable?

c. Essential questions: What questions will foster inquiry, understanding, and transfer of learning?

d. What key knowledge and skills will students acquire as a result of this unit or series of lessons? What should they eventually be able to do as a result of such knowledge and skills?



2. Assessment Evidence a. Performance tasks: Through what authentic performance tasks

will students demonstrate the desired understandings? By what criteria will performances of understanding be judged?

b. Other evidence: Through what other evidence (such as quizzes, tests, writing prompts) will students demonstrate achievement of the desired results? How will students reflect upon and self-assess their learning?



3. Learning Plan a. Learning activities: What learning experiences and

instruction will enable students to achieve the desired results?


5 Characteristics of Tasks that Affect Student Learning

Introduction of new topics with a problem-solving task

Use of communication strategies Connections across topics Development over time Tasks that challenge


Underlying Learning Theory

Problem-solving focus Introduction of topics with problem solving Inclusion of non-routine and application problems Use of higher-order thinking questions



Use of communication strategies Reading Writing Speaking Critical listening Multiple representations



Connections across topics Links to previous understandings Use of threads or strands through all topics Multiple, linked objectives taught concurrently to

eliminate isolated and fragmented teaching



Allow time to learn 3–8 days of development for a new topic 8–11 days of repetition Problems change qualitatively over time, not the

same type repeated



Tasks that challenge Use open-ended questions to allow a wide group

of students the opportunity to engage in the question or problem


”A child’s zone of proximal development is the distance between his actual development level as determined by independent problem solving and his potential development as determined through problem solving under adult guidance or in collaboration with more capable peers.”

L.S. Vygotsky

Mind in Society: The Development of Higher Psychological Processes

Optimal learning

hard

easy

Comfortable


Curriculum materials

Select a chapter in your curriculum materials.

Find instances or evidence of the 5 characteristics of learning tasks. Be able to support your examples.

Which criteria appear to be missing?


Continuous models for fractions

Continuous models for fractions:

Continuous models could be related to length, area, volume or mass.

The quantity represents .

25


Discrete models for fractions Discrete models:

Discrete models are typically sets of objects.

This represents (ratio of purple to the total).

25


Benchmark Fractions

12

Provide a referent for estimating size of fractions

0 1


56

9

40

79

43

815

211

1920

613

50110

1

14

893

1229

37

1417


Curriculum materials and fractions

Using your curriculum materials, discuss the following:

How are fractions introduced or reviewed?

Are both continuous and discrete models used?

How are the models connected or related for students?


34

58

1516

58

Fraction computations: Addition and SubtractionUsing the benchmark fractions, estimate the sum and difference of the problems:


34

58

1516

58

Using the rulers we created, perform the operations of the problems below.Be able to explain the actions you used on the ruler to get the sum or difference.


Perimeter and Area

Using the 24-inch long string as the edge, create as many rectangles as you can.

Measure the sides and record their dimensions in a table like the one below.

Dimensions Perimeter Area


Perimeter and Area



What patterns do you notice?

Dimensions Perimeter Area 1 X 11 24 units 11 square units 2 X 10 24 units 20 square units 3 X 9 24 units 27 square units 4 X 8 24 units 32 square units 6 X 6 24 units 36 square units


Perimeter and Area

How many rectangles can be made with an area of 36 square units?

Use the 36 tiles and find all the rectangles you can.


Perimeter and Area Recording Table



What patterns do you notice?

Dimensions Perimeter Area 1 X 36 38 units 36 square units 2 X 18 40 units 36 square units 3 X 12 30 units 36 square units 4 X 9 26 units 36 square units 6 X 6 24 units 36 square units


Perimeter and Area

What can you say about the relationships between area and perimeter?


Rectangle Area

Use base X height rather than length X width.


Parallelogram Area


Triangle Area


Trapezoid Area


Measurement Strand

What do you notice, as you look across the grades in the measurement strand of the framework, about the progression of the development of measurement formulas?


Comparison to Textbooks

How does the development of area and perimeter in your textbook compare to the curriculum framework?

How is the development we did with area and perimeter similar to your textbook?

How is the development we did with area and perimeter different from your textbook?


Closing focus questions

What are key components of the curriculum framework?

Decide at your table what you consider to be critical ideas.

What questions remain about the framework?

Documents

2007 Mississippi Department of Education 2007 Mississippi Mathematics Framework Training Revised (Grades K-5) Day 2