Robert J. Riehsrobert.riehs@doe.state.nj.us

February 2012

OVERCOMING SPEED BUMPS IN THE TRANSITION

to the Common Core State Standards in MATHEMATICS

IN MATHEMATICS

“Speed bump” should be interpreted as a synonym for “challenge.” These speed bumps should be thought of less as obstacles than as challenges, which necessitate caution and careful planning.

Jaredand Corin

Speed Bumps

Practices/Content

The challenge of merging the Mathematical Content

Standards with the Standards for Mathematical

Practice

Jaredand Corin

Speed Bumps

Details

"The devil is in the details."

Details 

Subtleties 

Particulars 

Nuances

Whether you modify the old curriculum one step at a time, or you throw it all out and start afresh, there are potential speed bumps

Details 

Subtleties 

Particulars 

Nuances

3.MD.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters.(At grade 4, a related standard this includes eighths of an inch.)

Details 

Subtleties 

Particulars 

Nuances

3.MD.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters.(At grade 4, a related standard this includes eighths of an inch.)

The line plot below shows the test scores of 26 students:

3.MD.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters.(At grade 4, a related standard this includes eighths of an inch.)

--Arizona Department of Education

One of the Common Core High School Clusters:

Solve systems of equations

Details 

Subtleties 

Particulars 

Nuances

One of the Common Core High School Clusters:

Solve systems of equations

A.REI.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x2 + y2 = 3.

Whether you modify the old curriculum one step at a time, or you throw it all out and start afresh, there are potential speed bumps

Details 

Subtleties 

Particulars 

Nuances

Things we shouldn’t forget… Grades 2, 3, and 4

The importance of actually measuringNEW Grade 2 CCSS 2.MD.1 Measure the length of an object by selecting and

using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. [2.MD.9 limits this expectation to the nearest whole unit.]

CCSS 2.MD.6 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram.

NEW Grade 3 CCSS 3.MD.4 Generate measurement data by measuring lengths

using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters. [In grade 4 (CCSS 4.MD.4), the expectation is extended to include eighths.]

Things we shouldn’t forget… Grade 5

Adding & subtracting decimals includes decimals and whole numbers

NEW Grade 5 CCSS 5.NBT.7 Add, subtract, multiply, and divide

decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Example:Paula’s tractor holds 3 liters of gasoline. Tom’s tractor holds 2.4 liters. How much more does one tractor hold than the other?

[Not money - Not Multiple Choice]

2.4 3 3.0─ 3 ─ 2.4 ─ 2.4

Things we shouldn’t forget… Grade 6

Various types of questions can be linked to the same standard

NEW Grade 6 CCSS 6.NS.7 Understand ordering and

absolute value of rational numbers. (there are bullets)

Example:

Find a number that is between 1/3 and 0.36.

Example (contextualized):

Mark and Tom played little league baseball last summer. Mark was at bat 33 times and had 11 hits. Tom had a batting average of .360. Find another possible batting average that is better than Mark’s but not as good as Tom’s.

Example (student-developed context):

Find a number that is between 1/3 and 0.36, and describe a situation in which you might actually need to answer such a question.

Things we shouldn’t forget… Grade 7

There are percents greater than 100

NEW Grade 7 CCSS 7.RP.3 Use proportional relationships to solve

multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

Example:

Dottie’s Teacher told her that when he started teaching in 1970 he could purchase a gallon of regular gasoline for his car for approximately 30¢. Now, in 2004, a gallon of gasoline costs approximately $1.80. What is the percent increase in price?

Misunderstanding: Understanding:1.50/.30 = 5% 1.50/.30 = 5 = 500%1.80/.30 = 6%.30/1.50 = .2 = 20%

Things we shouldn’t forget… Grade 7There is more to mathematics than

substituting into formulas

NEW Grade 7 CCSS 7.G.2 Draw (freehand, with ruler and protractor, and

with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

Example:

The hypotenuse of a right triangle has a length of 34 centimeters. Which of the following could be the perimeter of the triangle?

a. 20 cmb. 50 cmc 80 cmd. 110 cm

34cm

Things we shouldn’t forget… High School/Grade 7There is more to mathematics than

substituting into formulas

NEW Grade 7 CCSS 7.G.4 Apply geometric methods to solve design

problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).★

Example:

Jennie has a souvenir baseball, which she wants to store in a cubical box. She knows that a baseball is 2 3/4" (7 cm) in diameter. What would be the smallest possible dimensions for a cubical box that Jennie could use to store her baseball?

Misunderstanding: Understanding:(4/3) πr3 ≈ 179.6 cm3 Edge of box = 7 cm Edge of box ≈ 5.65 cm Edge of box = 2 3/4"(4/3) πr3 ≈ 10.89 in.3

Edge of box ≈ 2.22 in.

Speed Bumps

15%

15%

Some have the misconception that the mathematics in the Common Core is all the mathematics there is to learn. Avoid this speed bump! Take advantage of the district’s prerogative to add additional content.

Others are tempted to try to include all or nearly all that they have taught in previous years. Avoid this speed bump also! Don ’t lose focus

Mathematics | Grade 3In Grade 3, instructional time should focus on four

critical areas: (1) developing understanding of multiplication and

division and strategies for multiplication and division within 100;

(2) developing understanding of fractions, especially unit fractions (fractions with numerator 1);

(3) developing understanding of the structure of rectangular arrays and of area; and

(4) describing and analyzing two-dimensional shapes.

Mathematics | Grade 4In Grade 4, instructional time should focus on three critical

areas: (1) developing understanding and fluency with multi‑digit

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

(2) developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers;

(3) 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.

Some have the misconception that the mathematics in the Common Core is all the mathematics there is to learn. Avoid this speed bump! Take advantage of the district’s prerogative to add additional content.

Others are tempted to try to include all or nearly all that they have taught in previous years. Avoid this speed bump also! Don ’t lose focus

Potential Challenges in Transitioning to the Common Core in Mathematics

Common Core State Standards (CCSS) adopted June 16, 2010

Grade/ Course

Change

1.NBT.3. Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

Gr. 2

CCSS move symbols ( = , < , > ) from grade 3 (NJ cccs 4.3.3.D.2) to grade 1.

2.OA.3. Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. Gr. 3

CCSS move “determining whether a whole number is odd or even” from grade 3 (NJ cccs 4.1.3.A.3) to grade 2.

2.NBT.4. Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.

CCSS move symbols ( = , < , > ) from grade 3 (NJ cccs 4.3.3.D.2) to grade 2 (actually grade 1, in 1.NBT.3).

3.OA.7. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations.

By the end of Grade 3, know from memory all products of two one-digit numbers.

Gr. 4CCSS move memorizing the multiplication table from grade 4 to grade 3

Speed Bumps

Transition

Transition

Measuring AnglesAn Example of a Challenge in the

TransitionGrade 4 Grade 5

Cohort 1

2010-11 Old State Standards 2011-12 Old State Standards (Includes Measuring

angles in grade 5)

Cohort 2

2011-12 Old State Standards 2012-13 CCSS

Measuring angles (?)

Cohort 3

2012-13 CCSS4.MD.5. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement.

2013-14 CCSSMeasuring angles was learned in grade 4.

4.MD.6. Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

Overcoming speed bumps during the transition to the Common Core State

Standards in Mathematics

Prioritize interweaving the practices with content.

Pay attention to details in the CCSS. Focus on critical content areas. Build in adjustments during the transition.

Questions?Prioritize interweaving the practices with content.

Pay attention to details in the CCSS. Focus on critical content areas. Build in adjustments during the transition.