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Donna Parrish Using the Math Standard to Enrich Instruction Oregon’s Second Annual GED Summit Creating Promise, Designing Success

Warm-up: Talk with a neighbor about how the math portion of the 2014 Series of the GED is different from that of the 2002 Series. Jot down some one-word descriptors.

Think about a skill that you, as an adult, learned. That skill might be baking, painting, skiing, knitting, playing pool, building a deck…anything. Consider how you went about learning that skill. Jot down a few words to answer the following then share your answers with a neighbor. What was the motivation for learning the skill? What was the setting? What steps did you take to master the skill?

What commonalities did you find in our adult learning? What do our own learning experiences tell us about the way our students learn? Compare what we know about adult learning with the way you were taught math and/or the way math is typically taught in our programs.

Components of the Oregon Math Standard = Important Aspects of the Problem-Solving Process Though the components are numbered in this presentation that does not imply they are used sequentially. Individuals move back and forth among the components as they use their skills to solve problems.

1. Identify a question or situation that can use a mathematical approach.

2. Apply life experiences and knowledge of math concepts, procedures, and technology to figure out how to answer a question, solve a problem, make a prediction, or carry out a task that has a math dimension.

3. Identify information needed for the situation, including distinguishing between relevant and irrelevant information.

4. Understand, interpret, and work with concrete objects and symbolic representations (e.g., pictures, numbers, graphs, computer representations).

5. Determine the degree of precision best suited to the situation.

6. Estimate to predict results and to check to see if results are reasonable.

7. Communicate reasoning and results in a variety of ways such as words, graphs, charts, tables and algebraic models.

What are the math content strands? (There are four of them.)

Hint: One of them is Geometry and Measurement

Patterns, Functions, and Algebraic Reasoning

Data and Statistics

Number and Operation Sense

Now let’s consider what a fraction like ½ means. First recall the context or setting where you used this very well- loved fraction, then talk with a partner or two about what the fraction ½ meant in your situation.

One whole divided into 2 equal parts and we have 1 of those equal parts.

A division problem - one divided by 2 2 ) 1

A ratio or comparison (1 out of every 2 widgets was dark brown)

The name of a point on a number line or measurement. The board is about ½ foot long.

The part of a group or set meaning - does not involve cutting a whole into equal parts. Nor does it involve a natural whole. The part of a group meaning involves selecting objects from a group on some basis. A group is not a natural whole as is a pie (for example). Unlike the “cut” meaning, the part of a group meaning does not require that the objects be of the same size or type. (1/2 of the books are flat on the floor)

What assumptions do we make about our students’ understanding of the meaning of fractions?

Think about your favorite number. On the sticky note, use that number to make a fraction that is equal to 1. You may use any of the ways of thinking about what a fraction means.

Did anyone write a fraction whose numerator and denominator are different numbers?

Let’s take a moment to post our fractions on a number line. Please come up and put your 1 in the correct spot. If there is already a sticky note where you need to post yours, place yours above the one that is already there, making it touch the previous one.

We just made a line plot. What conclusions can we draw from that plot?

All our sticky notes were the same size and there were not very many of them. What would we need to change if there were 500 sticky notes?

What if someone’s favorite number is 3.14? What would the “one” (or unit) fraction look like? Where would that fraction go on the line plot?

Take a moment to write statement about what “one” looks like as a fraction.

What strands were we just addressing?

Let’s think about the role of the number 1 in multiplication. What happens when we multiply a number by 1?

Can we generalize or “algebrafy” that multiplication (1 x any number = the number you started with). 1 X = OR x 1 =

How would you name the multiplying by one relationship? Are there any other big ideas in that relationship?

Now let’s put two big ideas together (what fractions are equivalent to 1 and what happens when we multiply by one).

Sometimes it is helpful to draw a big one around fractions that are equivalent to 1.

x =

x =

x = AND SO ON…

Is that how you were taught to change denominators or did you learn the “guzinta” method? Consider rote procedure versus building understanding.

The CCRS Requires Three Shifts in Mathematics 1. Focus : Focus strongly where the standards focus. 2. Coherence: Designing learning around coherent progressions level to level 3. Rigor: Pursuing conceptual understanding, procedural skill and fluency, and application — all with equal intensity

Changing gears again, let’s think about graphing fractions. WHAT???Nobody ever graphs fractions?

1.Please get your graph paper and draw two axes on it. Something like

Put a small circle at the origin, then label the horizontal axis with the word “denominator” and number the axis as far as you can. Label the vertical axis with the word “numerator” and number that axis.

How might the plot for all the fraction equivalents be used? Discuss your ideas with a partner.

Use your graph to determine what numerator should pair with a denominator of 7. What is the numerator for an equivalent of ½ that has a of 13?

Does graphing these fractions lay groundwork for something that comes a little later in the math curriculum? Hint: y=mx + b

What does a fraction that is equivalent to 1/2 look like? Can you make a general rule?

How could this graph be used to order fractions from least to greatest (or vice versa)? What typical algebra topic are we approaching?

How is teaching fractions based on the ideas presented here different from the typical workbook approach?

Which strands In this sample lesson did we touch on? Which components of the standard did we address? Which strands did we not address?

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