Critical Areas for 3-5What do our students have to master?

NormsCourtesy

Be on time

Cell phones on silent, vibrate, or off

Be mindful of side-bar conversations

Focus on the task at hand

Collaborative

Promote a sense of

inquiry

Frame meaningful

questions

Pay attention of self and

others

Assume positive

intentions

Be reflective

Today’s OutcomesParticipants will have a better understanding of

the critical areas in 3rd Grade.

Participants will have a better understanding of the critical areas in 4th Grade.

Participants will have a better understanding of the critical areas in 5th Grade.

Participants will have a better understanding of the progression of skills through the grade levels.

3rd Grade Critical AreasDeveloping understanding of multiplication

and division and strategies for multiplication and division within 100.

Developing understanding of fractions, especially unit fractions (fractions with numerator 1).

Developing understanding of the structure of rectangular arrays and of area.

Describing and analyzing two-dimensional shapes.

4th Grade Critical Areas Developing understanding and fluency with

multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends.

Developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers.

Understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.

5th Grade Critical AreasDeveloping fluency with addition and

subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions).

Extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations.

Developing understanding of volume.

3 Areas of Number SenseWhole NumberFractions/Decimals

Geometry

What do these look like at your grade level and how do they progress to the next grade

level?

How much film? An army bus holds 36 soldiers.

If 128 soldiers are being bused to their training site, how many buses are needed?

Be prepared to share your strategy. How it fits the critical areas of your grade level.

How many times can you take ½?

To encourage people to attend a special concert, radio station MATH decides to give out 1242 free tickets in the following manner. Each day the station will give away half of the tickets in its possession. How many days will it take before MATH has only one ticket to give?

Fencing TaskMs. Brown's class will raise rabbits for their

spring science fair. They have 24 feet of fencing with which to build a rectangular rabbit pen to keep the rabbits.

If Ms. Brown's students want their rabbits to have as much room as possible, how long would each of the sides of the pen be?

How would you go about determining the pen with the most room for any amount of fencing? Organize your work so that someone else who reads it will understand it.

How many rectangles?

Once you solve this problem, think how it progresses through the critical areas of all 3 grade levels. With your group list the progression of skills that could be covered.

Problem SolvingIf Math was taught with words, then word

problems would be easy.

• How can we use this quote when we are thinking about how to plan our instruction?

• Why don’t we just teach the algorithm or key words?

• How can different problem types help?

How are these 2 problems different and how will students think about

them differently?

I have seven apples and Carla has four apples. How many more apples do I have than Carla?

I had seven apples and ate four apples. How many apples do I have left?

Turn and talk

Problem Types Which problem types do you most often see in

a typical text book and how can you assure that all problem types are mastered?

Look at the multiplication and division situations. How are they different and how do they progress in difficulty.

Where do fractions fit into these situations?

Turn and talk.

Problem Types• Equal Groups

• Arrays/Area

• Compareo Unknown Producto Group Size Unknowno Number of groups unknown

Equal Groups• There are 15 cars in the parking lot

and each car has 4 tires. How many tires in all?

• Roles aren’t interchangeable• Easier to model with pictures or

repeated addition

Array/Area

• Simon arranged chairs in the gym for an assembly. He put 42 chairs into 6 equal rows. How many chairs were in each row?

• Partitive division: How many in each group.

• I have 24 apples are arranged into equal rows. How many rows will I be able to fill if I put 3 apples into each row?

• Quotitive division: How many groups

Compare• Elizabeth read 48 books during the

summer vacation. This is four times as many as Catherine. How many books did Catherine read during summer vacation?

• Language is issue, students need modeling and a way to represent the problems

• Together, Jasmine and Laura earned a total of $64 babysitting. If Jasmine earned $14 more than Laura, how money did each girl earn?

Important questions to ask:

• What is the problem describing?

• How can you write it down?

• How can you find the answer?

• What other questions should we ask our students?

Let’s Write Some ProblemsAt your tables take some time

to write your own grade level problems that cover all of the problem types and your critical area content.

We need to Stop Teaching and Start Coaching.

Numbers and Strategies Should Be Flexible and Build Upon One Another.

Questions or Concerns?

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