Now we have a program that provides extra support through a differentiated core program, preview program, and response to intervention. While all three programs have merit, they don't offer the consistent, daily developmental math program that strugglers need. As Khan suggests in his Ted Talk, we need to help these students catch up by mastering early math skills which provide a child with a strong number sense foundation and mastery for later learning.
Jo Boaler would suggest, in part, using meaningful math projects that naturally help a child to learn these skills in engaging ways. Her "floor to ceiling" explorations allow all students to learn in meaningful, collaborative waysways that don't separate those with strong skills and those with weaker skills.
I really like this idea, but right now with our tight gradelevel standards expectations that's difficult to employ at all times. Instead, I think what we should do is provide a two session a day program including a differentiated core program for all that employs lots of meaningful math projects and differentiated learning events and a fiveday a week number sense program.
Core program time would equal about 45minutes a day while number sense programming would equal another 3045 minutes. During number sense grouping, students would mostly stay in same groups with those who struggle the most with number sense assigned to smaller groups with highly qualified educators and those with stronger skills assigned to larger groups with teachers and/or teaching assistants. Those that struggle would begin at their level of need. For example, if a child could not make combinations of 10, then that's where that child would start and build from there. I would use the list of number sense skills, concepts, and knowledge below to lead the assessments and groups. I created this list from research.
This two session a day math program would meet both the need for students to engage in meaningful, heterogenous math groups while also providing sensitive teaching and coaching related to developing students strong number foundation which is essential for more sophisticated math learning. This kind of programming would provide the consistency, daily practice, and successful coaching that allows students to build one skill on top of another as they move forward in math. The change to the current program would be to combine the preview program and RTI into one five to six day a week number sense developmental program. In this way students would have the chance to develop skill in a brainfriendly way, a way that allows them to see how once concept, skill, or knowledge point leads to another. This kind of learning develops a strong math disposition because math learners are pattern seekers and relationship finders. Programs that are less consistent and coordinated do not naturally match the ways our brains work to gain depth, fluency, and mastery over topics.
Ladder One  Counting
Write out the numbers in each level, then practice counting forward and backward. Let a family member test you by listening to you count the level without looking at your paper.
Level
(each level should be achieved forward and backward)

Notes/Date Passed

up to 25
 
to 100 by ones
 
to 100 by 10's
 
to 100 by 5's
 
to 100 by 2's
 
to 20 by 1/2
 
to 20 by 1/3
 
to 20 by 1/4
 
to 20 by .1
 
to 20 by .5
 
to 1,000 using number booklet
 
to 10,000 by 1000's
 
to 10,000 by 100's
 
to 10,000 by 10's


Ladder Two: Math Facts, That Quiz: http://www.thatquiz.org/
You pass a level when you can answer 50 facts in three minutes or less.
Fact Level
(students highlight fact set that they are currently working on)

List Time, Error #, and Date each Time you Take the Test. Move to next level when you pass.

addition facts 112
 
subtraction facts 112
 
addition/subtraction facts 112
 
multiplication facts 112
 
division facts 112
 
multiplication/division facts 112
 
multiplication/division/add/subtraction 112

Ladder Three  Computation (paper/pencil tests)
Name: _______________________________________________________________________
Large Number Computation

Test Date, Error Notes, Time

Large Number Addition including decimals, more than two addends, money, 4digit by 4digit, carrying, and checking with estimation.
 
Large Number Subtraction including decimals, money, 4digit by 4digit, borrowing, and checking with addition.
 
Large number multiplication including 2digit by 3digit, decimals, money, and checking with estimation.
 
Large number division including 3digit divided by 1digit and 2digit and checking with multiplication.

Large Number Computation Test: Addition
Exact Solution

Estimated Solution

75 + 89
 
129 + 2,357 + 6,890 + 24,679
 
2.9 + 4.08 + 3.45 + 12
 
6,789,234 + 6,789,235
 
$65.78 + $298.78 +$587
 
78,967 + 35,567 + 67,987

Large Number Test: Subtraction
Exact Solution

Checking Solution with Addition

894  231
 
8,213  6,989
 
$295.78  $198.39
 
7.8  2.12
 
758,221  679,989

Large Number Multiplication Test
Exact Solution

Estimated Solution

78 X 5
 
67 X 29
 
129 X 87
 
$45.67 X 8
 
7.8 X 2.31

Large Number Division Test
Exact Solution

Check with Multiplication

89  3
 
78/4
 
389  8
 
6,789  9
 
879  23

_________________________________________________________________________________
Ladder Four
Essential Fourth Grade Skills
That Quiz: http://www.thatquiz.org/
Skill

Time

Time/Error/Date/Teacher Sign

Integers: Number Line L4

50  10 minutes or less
 
Place Value L3

50  10 minutes or less
 
Place Value L6

50  10 minutes or less
 
Integers: Inequality L3

50  5 minutes or less
 
Integers: Inequality L5

50  5 minutes or less
 
Integers: Inequality Add L12

50  10 minutes or less
 
Integers: Inequality Subtract L12

50  10 minutes or less
 
Integers: Inequality Multiply L12

50  10 minutes or less
 
Integers: Inequality Divide L12

50  10 minutes or less
 
Integers: Exponents L2

50  5 minutes or less
 
Algebra L2

50  10 minutes or less
 
Algebra L3

50  10 minutes or less
 
Measure L2 Both inch + cm

50  10 minutes or less
 
Measure L3 Both inch + cm

50  10 minutes or less
 
Money L7

50  10 minutes or less
 
Time: Simple Clocks L4

50  10 minutes or less
 
Time Passed L2

50  10 minutes or less
 
Graphs: Bar and Line L2

25  10 minutes or less
 
Geometry Shapes L3

50  10 minutes or less
 
Geometry Triangle
Perimeter L10

25  10 minutes or less
 
Geometry Perimeter
Rectangle L12

25  10 minutes or less
 
Geometry Cube Volume
L5

25  10 minutes or less
 
Fraction Identity L 10

50  10 minutes or less
 
Fraction: Inequality L3

50  10 minutes or less
 
Fraction: Simplify L3

50  10 minutes or less
 
Fraction: Arithmetic add L1

50  10 minutes or less
 
Fraction: Arithmetic subtract L1

50  10 minutes or less
 
Place Value: Decimals L3

50  10 minutes or less
 
Probability  level 1

15  3 minutes or less
 