2007 Mississippi Department of Education 2007 Mississippi Mathematics Framework Revised Training...

2007 Mississippi Department of Education

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

Day 1


Select the number of times per week that you’d like to have chocolate.

Multiply this number by 2. Add 5 to the product. Multiply your answer by 50. If you’ve already had your birthday this year,

add 1757. If you’re still waiting for your birthday, add 1756.

Subtract the four-digit year of your birth.

Sweet Thoughts


Definition of Problem Solving

The process involved to solve a problem or situation for which the individual who confronts it has no procedure that will guarantee a solution


Definition of Algorithm

A series of steps which, if followed correctly, will lead to a correct answer


What level of thinking is required by each task?

1. Temika earns 5 points for every homework assignment that is turned in on time. If she turns in homework on time for 6 days, how many points does she get?a. 20 b. 25 c. 30 d. 35

2. Courtney made a pattern with numbers. What is the next number in the pattern? 7, 16, 25, 34, _____a. 35 b. 37 c. 43 d. 44

3. Find the next three terms in the pattern and determine the rule for the following: 1, 4, 8, 11, 15, 18, 22, 25, 29, . . .

4. Find the next three terms in the pattern, determine the rule for finding the next number in the pattern, and find a model for the pattern:

1, 1, 2, 3, 5, 8, 13, 21, 34, . . .


Thinking Levels of Tasks

What is the cognitive demand of each task? Cognitive demand refers to the level of thinking

required by the task or problem. How are the problems alike related to

cognitive demand? How are they different?


Norman Webb’s Depth of Knowledge

Level 1 (Recall) recall information such as a fact, definition, term, or a

simple procedure perform a simple algorithm or apply a formula (one-

step, well-defined, and straight algorithmic procedure should be included at this lowest level)

Key words: identify, recall, recognize, use, and measure



Level 2 (Skill/Concept) engage in some mental processing beyond a habitual

response explain the purpose and use of experimental procedures;

carry out experimental procedures; make observations and collect data; classify, organize, and compare data; and organize and display data in tables, graphs, and charts

Keywords: classify, organize, estimate, make observations, collect and display data, and compare data (imply more than one step)



Level 3 (Strategic Thinking) reason, plan, use evidence, and engage in a higher level of

thinking than the previous two levels (require students to explain their thinking)

require students to make conjectures engage in activities that have more than one possible

answer and require students to justify the response they give draw conclusions from observations; cite evidence and

develop a logical argument for concepts; explain phenomena in terms of concepts; and use concepts to solve problems



Level 4 (Extended Thinking) require complex reasoning, planning, developing, and thinking

most likely over an extended period of time require high cognitive demands in the task and the work should

be very complex require making several connections—relate ideas within the

content area or among content areas—and select one approach among many alternatives on how the situation should be solved

include designing and conducting experiments; making connections between a finding and related concepts and phenomena; combining and synthesizing ideas into new concepts; and critiquing experimental designs


Curriculum materials and DOK

Each group has been given a DOK level.

Find instances or evidence of the characteristics of that level in your curriculum materials.


Number Development

Count out 15 tiles.

Discuss with your partner: how many different ways can you put the tiles into two groups? Note: disregard color.


Number Development

What if the number of tiles you had was 20 tiles?

How many groups do you think you could make?

Discuss with your partner to predict.


Part-Whole Diagrams for 15

15 15

1515 15

15

7 8


Fact Families

15 = 8 + 7

15 = 7 + 8

15 – 8 = 7

15 – 7 = 8

15

7 8


Number Development

Model 127 using your Base-ten blocks.

Record your solutions in a table like the one below.Flats Longs Units


Curriculum Framework

Using the curriculum framework, look at the objectives in the Number and Operations strand for the grade levels K–5.

At your table, decide which objectives the tasks we completed would address.

Are there any terms in the objectives that you’re not clear about? If so, highlight them. Write them on a post-it note and place it on the chart paper.


Framework and Textbook Comparison

Using your instructional materials, do you find evidence of these objectives?

Check to see how these objectives are developed.


Contexts for Computations

In pairs, you will write– Two word problems or contextual problems that

can be solved with addition Three word problems or contextual problems that

can be solved with subtraction


Review Problem Solutions

Were the problems solved in the way you had anticipated?

Why or why not?


Addition and Subtraction

1. Katie had 16 stickers. She bought 12 more stickers. How many stickers does she have now?

2. There were seven boys playing tag. Two boys went home. How many boys are still playing tag?

3. Tom has 5 brothers. Juan has 3 brothers. How many more brothers does Tom have than Juan?

4. Jesse has 14 golf balls. Teva has 23 golf balls. How many more golf balls does Jesse need to have as many as Teva?


Addition and Subtraction

1. Katie had 16 stickers. She bought 12 more stickers. How many stickers does she have now? (Combining)

2. There were seven boys playing tag. Two boys went home. How many boys are still playing tag? (Take-away)

3. Tom has 5 brothers. Juan has 3 brothers. How many more brothers does Tom have than Juan? (Comparison)

4. Jesse has 14 golf balls. Teva has 23 golf balls. How many more golf balls does Jesse need to have as many as Teva? (Missing addend)


Addition and Subtraction Actions

Consider the actions involved in addition and subtraction.

How are they related?

How are they different?


Curriculum Framework Comparison

Look at the Number strand in your grade level.

What do you notice about the objectives related to addition and subtraction and their relationship to these models?

How does student understanding build from grade to grade?


Addition and Subtraction Algorithms

Solve in at least three ways:

572 862 + 347 – 295


Multiple Algorithms

At your tables, discuss:

What are the advantages of using different algorithms?

What are the disadvantages of using different algorithms?


Algorithms in Textbook

What algorithms are stressed or developed in your book?

How are they alike or similar to the ones we discussed?

Were any different algorithms stressed in your text that we did not discuss?


Focus Questions

How were the topic developments today similar to or different from the way you thought about these ideas?

What do you notice about the objectives in the curriculum framework with regard to number and algebraic development?

What level of thinking does the topic development of this type promote?

2007 Mississippi Department of Education 2007 Mississippi Mathematics Framework Revised Training...

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