Five Easy Steps to a Balanced Math Program
From OpenContent Curriculum
Recommendations for Math Review
Format:
- Printed out for students or students copy from board
- Categories for problems labeled.
- Collect student papers each day to look at error analysis and student reflection.
- Levels 0-2 can be verbal responses, whiteboards, or manipulatives.
- Students must show work for each problem.
- The goal is to reach 5 problems; start with 3 if necessary.
- The entire Math Review Process should take approximately 15-18 minutes daily.
Processing Math Review:
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Levels 0-2
- Math Review Weekly Report
- Math Review Template
- Verbal response by students based on error analysis.
- Emphasize key ideas and mathematical vocabulary.
- Student reflection verbally or in writing each day.
Levels 3-11
- Student generated error analysis for each problem.
- Student reflection in writing each day.
- Initial modeling by teacher of error analysis.
Essential Categories for Vertical Alignment
Key Concepts per Level
Categories for Math Review
| Level 0-2 | Level 3-5 and Grade 6 (Integrated Mathematics I) | Grade 7+ | |||||||||||||
| Fractions | Part-Whole
ex: Shade ‚"3 of 4" Divide the shape into parts. Equal parts
| Equivalent, Operations
14/21 = 2/3 2/3 + 4/3 = 6/3 = 2
2/3 > 4/7
| Fractions/Decimals/Percent/Proportions
1/8 = x/32
13/5 divided by 11/7 13/5 x 7/11 = 91/55
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| Probability | Likely vs Unlikely
Choose from spinners, dice, bags of tiles Averaging Graphing | Pull from a set using dice, spinners, and chips
| Statistics/Probability (independent, dependent)
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| Geometry | Recognize shapes
Attributes Vocabulary (shapes, lines) Lines ‚rays, segments, points | Shape names, area, perimeter, circumference
Find the area of a 3x5 rectangle Find the perimeter of a 6x2 rectangle Find the area and circumference of a circle with radius = 3 | Basic Formulas (perimeter/area)
A = 1/2x8(10 + 16) A = 4(26) A = 104 cm2 | ||||||||||||
| Measurement | * Metric
| U.S./Metric, units
Time: elapse time base 60/12 6am to 10:30pm is how much time? | Unit Conversions ‚ time, length/area, US/Metric
3ft x 3ft = 9ft2 | ||||||||||||
| Multiplication | With 3 twos, how many do you have?
2+2+2= 3x2
Area
3x4 grids Skip counting (by 10's, 5's, 2's, etc.) | 2-digit, 3-digit, 10's
53 = 5x5x5
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| Division | Equal Sharing | Long division with remainder | Division of fractions | ||||||||||||
| Place Value | Groups of 10
Values of place (whole numbers) Decompose numbers | Reading decimal, expanded notation
Value of digits 1,234,567.59 underline the tenths place | Scientific Notation
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| Number Sense | * Anchors of 5 and 10
1+4=5, 2+3=5, 4+1=5, 3+2=5
| Anchor of 5 and 10
Inequalities Addition patterns Patterns in multiplication Basic facts | Less than, more than, less than or equal to, more than or equal to.
Reasonable answer | ||||||||||||
| Integers | Integers: Basic Operations
-6 x -2 = 12 4 x (-2) = -8 | ||||||||||||||
| Exponents | Exponents: Negative, Basic Operations
(-3)2 = 9 -32 = -9 |
Math Review Quiz Recommendations
- Every week (primary) or every other week (secondary).
- 2 questions for each category used in Math Review (6-10 questions).
- Grade papers together with students using error analysis and student reflection.
- Use quiz results for flex grouping.
- Use quiz results to change categories on Math Review.
Mental Math Recommendations
Frequency:
- 1-3 problems per day.
When:
- This can be done during transitions and math times.
Processing:
- Have students share out their reasoning to arrive at an answer.
- In Upper Levels have students record answers and occasionally reflect on progress.
Themes:
Problem Solving Recommendations
Elements of Problem Solving Tasks:
- Multiple steps
- Allows for various strategies to solve
Frequency:
- Two or more times a month.
- At least one problem solving task for each unit.
Format:
- In the table below are the recommended, district-wide forms and templates for problem solving.
- Start with small cooperative groups, using the Poster Method. Then move towards the more formal Alternative Method write-up.
Culturally Relevant Math Problems
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| Poster Method Steps
Kindergarten Level 1 Level 2 | Poster Method Steps
Alternative Problem Solving Task Write-up Individual Problem Solving (for assessment/independent problem solving) | Teacher/Student Expectations
Group Problem Solving Individual Problem Solving Task Write-Up Guide Individual Problem Solving (for assessment/independent problem solving) |
| | After doing individual work student are allowed to come up to the board and give “hints”.
Hint Process is:
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Problem Solving Rubrics
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Units of Study/Conceptual Units
The units of study will be broken down into groups:
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Click on the Level you are looking for.
Participants in Five Easy Steps Training
During CASC 2009
- Ryan Woodruff - rwoodruff@bssd.org
- Mary Huntington - mhuntington@skk.bssd.org
- Amy Norman - anorman@kts.bssd.org
- Eric Lowry - elowry@wbb.bssd.org
- Steve Alston - salston@shh.bssd.org
During Early August Workshop (2009)
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November Workshop
- Ryan Woodruff - rwoodruff@bssd.org
- Shon Bernard - sbernard@bssd.org
- Josh Bullock - jbullock@tla.bssd.org
- Donald Eldridge - deldridge@sva.bssd.org
- LaRee Eldridge - llindsey@sva.bssd.org
- Tracie Nash - tnash@wbb.bssd.org
- Amy Norman - anorman@kts.bssd.org
- Heidi Hargraves - hhargraves@bssd.org
- Scott Herrmann - sherrmann@sva.bssd.org
- Melinda Oxereok - moxereok@waa.bssd.org
- Mona Landrum - mlandrum@tla.bssd.org
- Brian Bailey - bbailey@shh.bssd.org
- Jessica Keller - jkeller@bssd.org
- Bonnie Pickner - bpickner@wbb.bssd.org
- Frank Amaktoolik - famaktoolik@glv.bssd.org
Resources
CASC 2009 book recommendations
