Category:5 Easy Steps to a Balanced Math Program

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Recommendations for Math Review

Contents

Format:

  1. Printed out for students or students copy from board
  2. Categories for problems labeled.
  3. Collect student papers each day to look at error analysis and student reflection.
  4. Levels 0-2 can be verbal responses, whiteboards, or manipulatives.
  5. Students must show work for each problem.
  6. The goal is to reach 5 problems; start with 3 if necessary.
  7. The entire Math Review Process should take approximately 15-18 minutes daily.


Processing Math Review:

Levels 0-2

Levels 3-11

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


Half Half1.png vs Half2.png vs Half3.png


Adding like fractions (with pictures)

Equivalent, Operations

14/21 = 2/3

2/3 + 4/3 = 6/3 = 2


Comparison

2/3 > 4/7


2/3 Draw a picture, show what 2/3 looks like

Fractions/Decimals/Percent/Proportions


1/8 = .125 = 12.5%

1/8 = x/32

Equation.gif

13/5 divided by 11/7

13/5 x 7/11 = 91/55


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)


P(2 spades) with replacement = 13/52 x 13/52 = 1/4 x 1/4 = 1/16


P(2 spades) without replacement = 13/52 x 12/51 = 1/4 x 12/51 = 3/51

Geometry Recognize shapes

Shapes.png

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)


Trapzd.png


A= 1/2 h(b1 + b2)

A = 1/2x8(10 + 16)

A = 4(26)

A = 104 cm2

Measurement * Metric
  • Time (analog)‚ telling time to the 1/2 hour, 1/4 hour
  • Calendar
  • Non-standard units
  • unifix cubes
  • longer, shorter
  • Standard units (inches, centimeters)
  • Weight


U.S./Metric, units


3ft = ___ inches

Time: elapse time base 60/12

6am to 10:30pm is how much time?

Unit Conversions ‚ time, length/area, US/Metric


How many square feet are in 1 square yard?


1yd = 3ft

3ft x 3ft = 9ft2

Multiplication With 3 twos, how many do you have?

2+2+2= 3x2


Repeated Addition

Area


3x4 grids

Skip counting (by 10's, 5's, 2's, etc.)

2-digit, 3-digit, 10's


Repeated multiplication

53 = 5x5x5


10x24 = 240

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


4.26 x 103=

Number Sense * Anchors of 5 and 10
  • Family groups

1+4=5, 2+3=5,

4+1=5, 3+2=5

  • Doubles
  • Position words (before, after, between, 1st, 2nd, 3rd, etc.)
  • Decomposed numbers
  • Quantities (model the number, more than, less then, equal to)
  • Addition patterns
  • Regrouping


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


-4 - (-3) = -4 + 3 = -1

-6 x -2 = 12

4 x (-2) = -8

Exponents Exponents: Negative, Basic Operations


4-3 = 1/43 = 1/64

(-3)2 = 9

-32 = -9

Math Review Quiz Recommendations

Mental Math Recommendations

Frequency:

When:

Processing:


Themes:

Level 0-2
Level 3-6
Level 7-9
Doubles, one more, one less, part/part whole relationships

Skip Counting

Addition/Subtraction

Money

Position Words

Fact Families

Patterns

Shapes

Time (calendar, days, months)

Story Problems

Background Knowledge (common knowledge, calendar, weeks, months, time)

Multiplication/Division

Repeated Addition

Repeated Subtraction

Inverse Relationships

Basic Facts (skip counting)

Doubles

Powers of 10 (Multiply)

Measurement Concepts

Fractions (Common Denominator)

Patterns

Money

Time

Measurement Conversions

Integers

Percents

Fractions

Square/Square Roots

Cube/Cube Roots

Geometry

Names and Attributes of Shapes

Problem Solving Recommendations

Elements of Problem Solving Tasks:

Frequency:

Format:

Culturally Relevant Math Problems

Level 0-2
Level 3-6
Level 7-9
Poster Method Steps

Kindergarten

Level 1

Level 2

Poster Method Steps


Student Product Expectations

Personal Data Sheet

Alternative Problem Solving Task Write-up

Problem Solving Task Summary

Individual Problem Solving

(for assessment/independent problem solving)

Individual Method Steps

Alternative Problem Solving Task Write-Up Guide

Teacher/Student Expectations

Group Problem Solving

Poster Method Steps

Alternative Method Steps

Individual Problem Solving Task Write-Up Guide

Individual Problem Solving

(for assessment/independent problem solving)

Individual Method Steps

Individual Problem Solving Task Write-Up Guide

Hint Process for Alternative Method
After doing individual work student are allowed to come up to the board and give “hints”.

Hint Process is:

  • Students are allowed to come up to the board and put up a hint to help with the problem. These can be anything the students deem helpful in solving the problem.
  • The teacher gets everyone else’s attention when the hint is put up, to allow that person to explain their hint.
  • Teacher does not validate or judge the hint.
  • Kids do not discuss, they just listen and decide for themselves if they want to use the hint or not.

Problem Solving Rubrics

BSSD Problem Solving Rubrics
Levels 0-2
Levels 3-6
Levels 7+
Download in PDF format
Download in PDF format
Download in PDF format
Download in OpenOffice format

Units of Study/Conceptual Units

The units of study will be broken down into groups:

Level 0-2
Level 3-6
Level 7+

Click on the Level you are looking for.

Participants in Five Easy Steps Training

During CASC 2009


During Early August Workshop (2009)

Levels K-2
Levels 3-6
Levels 7+



November Workshop

Resources

CASC 2009 book recommendations

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