1. Daily Cumulative Review and
2014
What’s New with K-2?
Daily Cumulative Review and
K-2 Updates
Denise Schulz NCDPI

2. Welcome “Who’s in the Room”
Survey participants: first timers, math coaches, classroom teachers, central office, principals, etc…
This will allow us to modify presentation accordingly.

3.
We will not use all slides but we have included additional slides for your convenience so that you may modify accordingly to your needs for a school or district.
Example: If used in PLC’s – may want to take one Practice Standard at a time and develop it more thoroughly.

5. Updates New version of the K-2 Assessment
Released the K-2 Assessment
Reformatted the K-2 Formative and Instructional Task wiki
Posted the K-2 Building Conceptual Understanding and Fluency Through Games

6. What does it mean to be Mathematically Proficient?
Discuss

7. Turn and Talk
Are students who can remember formulas or memorize algorithms truly mathematically proficient, or are there other skills that are necessary?
Is the correct answer the ultimate goal of mathematics, or do we expect a greater level of competence?
Discuss

8. For the first time, mathematical processes are elevated to essential expectations, changing our view of math to encompass more than just content. The goal now is to apply, communicate, make connections, and reason about math content rather than simply compute.
Increase attention on problem solving, discussion, and justification of thinking and decrease attention on rote practice, rote memorization of rules, and teaching by telling

9. Almost no student masters something new after one or two lessons or one or two homework assignments.
One student can’t remember the product of 9 and 7. A class forgets that there are 16 ounces in a pint and in a pound. It is apparent that isosceles is a long-forgotten term when it elicits only a sea of blank stares

10. The most effective strategies for fostering mastery and retention of critical mathematics skills and concepts is daily cumulative review.
Some teachers call it opening exercise or denotes it as daily launch strategies in their lesson plans. Others call it daily warm-ups or mini-math. Whatever the labels, it’s a daily, quick, systemically considered assessment that creates an immediate focus – it could be on just one or two word problems written on the board or flashed on a screen: other days it is seven quick oral questions; and the others days it is five written questions to get things going. But over the course of the week it is a chance, depending on the grade or class to address a number of facts of the day, an estimate of the day, a term of the day, a skill of the day, a picture of the day, and/or a measurement of the day

11. Number your paper one to five_
Consider the start of the class. As soon as the math time starts, you announce, “Number from one to five.” Already your class understands that you don’t waste time dilly-dallying around.
Your students now know that today’s mini-math is a five-item oral quiz, and based on the routines you’ve established, your students know that you’ll read each question twice as you wander around the room checking each students completed homework.

12. Mini Math
Charlie has 9 apples. His mom gave him 5 more. How many apples does he have?
What number is the same as 5 tens and 7 tens?
What number is 10 less than 83?
Draw a rectangle and partition it into 3 parts.
About how long is this pencil in centimeters?
In second grade, to launch the class, a mini-math review might look like:… Share slide

13. Planted 9 + 8 into memory banks as preparation for tomorrow.
1. Charlie has 9 apples. His mom gave him 5 more. How many apples does he have?
Taken affirmative action on fact mastery by testing a fact using mental strategies
Ascertained the number of students who still don’t have a command of this fact
Provided, if appropriate, positive reinforcement about the progress your class is making
Planted into memory banks as preparation for tomorrow.
You started with this question because you know that some of your students are still struggling with harder facts.
Ask how students solved the problem. Since you are walking around, you can see several strategies in place. Did students draw a picture? Are they counting on their fingers?
Since students have switched papers, a simple, “Raise your hand if the answer is not 14, quickly and accurately tells you how many students are still struggling with When it’s down to just a few or even none, consider the positive reinforcement and foreshadowing of “Great progress. We’re down to only two of you having problems with By the way, the first question tomorrow will be And the sum is …?”
Within the first minutes of your class, you’ve…..(share slide)

14. Three children were playing in the sandbox
Three children were playing in the sandbox. Two more children came to play in the sandbox. How many children are in the sandbox now?
Luis ate 4 grapes for a snack. He ate more grapes at lunch. If Luis ate 12 grapes in all, how many did he eat at lunch?
There were some children on the school bus. Then, 5 more students got on the school bus. Now, there are 14 students on the school bus. How many students were on the school bus to start with?

17. 2: What number is the same as 5 tens and 7 tens?
Emphasized place value strategies for adding within 1000
Reviewed that when adding, one adds tens and tens and sometimes it is necessary to compose hundreds
Recognized that a topic taught one month earlier needs periodic attention and reinforcement
Supported and gradual development of number sense for all students.
You added this question because it has been a month since you finished place value instruction. You understand that a deep sense of place value emerges from more than questions like “What digit is in the tens place?” and “what is the value of the 8?”
After quickly checking to see that most of your students have correctly answered 120, you can follow up with questions like “How did you determine the answer?” If many students miss this question, you can follow up with questions like “okay, so how can you model this to help you determine an answer?”
–questions that are much more difficult but capture a deep understanding of place value.
With questions like this, you have…..(share slide)

18. I am going to show you a card with dots on it
I am going to show you a card with dots on it. Quickly, tell me how many dots you see without counting.

19. I am going to show you a card with dots on it
I am going to show you a card with dots on it. Quickly, tell me how many dots you see without counting.

20. I am going to show you a card with dots on it
I am going to show you a card with dots on it. Quickly, tell me how many dots you see without counting.

21. I am going to show you a card with dots on it
I am going to show you a card with dots on it. Quickly, tell me how many dots you see without counting.

22. I am going to show you a card with dots on it
I am going to show you a card with dots on it. Quickly, tell me how many dots you see without counting.

23. I am going to show you a card with dots on it
I am going to show you a card with dots on it. Quickly, tell me how many dots you see without counting.

24. I am going to show you a card with dots on it
I am going to show you a card with dots on it. Quickly, tell me how many dots you see without counting.

25. I am going to show you a card with dots on it
I am going to show you a card with dots on it. Quickly, tell me how many dots you see without counting.

26. I am going to show you a card with dots on it
I am going to show you a card with dots on it. Quickly, tell me how many dots you see without counting.

29. 3. What number is 10 less than 83?
Broadened place value to an understanding of 10 or 100 more and less than a given number and set the foundation for further exploration
Emphasized place value strategies in mentally adding 10 to a given number
You understand that students need a deep sense of place value.
After quickly checking to see that most of your students have correctly answered 73, you can follow up with questions like “what digit did you change and why?”
If many students miss this question, you can follow up with questions like “okay, so what number is 10 more than 83?” If most students find this easy, you know you can challenge your students with questions requiring addition that involves changing the digit 9 to a 0 (“what number is 10 more than 94?”) or subtraction that involves changing the digit 0 to a 9 (what number is 10 less than 105)–questions that are much more difficult but capture a deep understanding of place value.
With questions like this, you have…..(share slide)

31. Today we are going to play The Mystery Number Game
Today we are going to play The Mystery Number Game. I am going to give you some clues which will help you figure out each mystery number.
Here is your clue. I have 10 and 2 more. Write the mystery number in the first box.
Let’s try another one. Here is your clue. I have 10 and 5 more. Write the mystery number in the box with the number 2.

34. 4. Draw a rectangle and partition it into 3 parts.
Concretizing the mathematics by means of pictures and visualization
Clear misunderstandings by analyzing drawings
One of the most powerful tools we have to help students develop conceptual understanding of key mathematical ideas in concretizing the mathematics by means of pictures and visualization.
Just as the use of representations is a critical component of all good instruction, this question is the perfect opportunity to reinforce this idea. It’s amazingly informative to see what proportion of your class correctly partitions into thirds. It’s humbling to see how many create equal-sized thirds and how many still fail to understand this critical piece of the fraction puzzle.
If there is time, or if there is clear misunderstanding, follow up with, “please describe the picture on the paper in front of you.” When one student says, “Divide the rectangle into three parts,” you could divide the rectangle in half and then divide one of the halves in half to lighten things up as well as raise the issue of equal parts.
It’s also amazing how much geometry can be reviewed (and even taught) when students must describe the pictures that one of their classmates has created.

38. When asked “What is ¼. ” One child said that ¼ was a “little pie shape
Extending Children’s Mathematics, pg. 4

41. In each square record a different way you can divide the square into four equal pieces (fourths).

42. In each square record a different way you can divide the square into four equal pieces (fourths).

43. 5. About how long is this pencil in centimeters?
Measurement is often the lost strand of the mathematics curriculum
Reinforce the concept of estimation and length units
Students need multiple opportunities to estimate and establish referents
Measurement is often the lost strand of the mathematics curriculum. And if measurement is lost, metric measurement is missing in action altogether. Because we’re looking for understanding and for ballpark estimates of these measures, you could provide a reasonable range and announce that any answer between ____ and _____ gets full credit. Gradually, over the course of the year, and depending on what is being measured and what units are being asked for, you can reduce the range of acceptable answers.
Remember estimation is about reasonableness. Estimation skills are related to the ability to substitute a nice number for one that is not so nice. The substitution may be to make a mental computation easier, to compare it to a familiar reference, or simply to store the number in memory more easily (Van de Walle). We know that we live in a world where estimation is the way in which smart kids show that they’re smart. We know that they often use estimation to outsmart the test by eliminating ridiculous answers. We also know that the weaker kids are often taught – to their detriment-that there is a correct procedure to arrive at estimates. In the same way that there are correct computational procedures.
Children develop a strong sense of number and measurement when they have real world referents to visualize mathematical abstractions. Estimation provides a starting point for constructing some of these early reference points.
Then expect students to grade the paper they’ve been given from 0 to 5 and hand it back to the student whose paper it is for a quick glance, and then collect the batch for your own quick glance.

44. Describing Attributes (Describe 2)
Accept any measureable attribute. Possible ideas include, but are not limited to:
 How long
 How wide
 How deep
 How tall
 How much water it will hold
 How many fish will fit
 How cold/hot the water is
 How much it weighs

47. Commit to helping students visualize mathematics
Another way to view the 5 to 8 minutes allocated to this daily activity is to consider that 5 minutes x 180 days equal 900 minutes, or 15 hours!
You know that you can change the world in 15 hours.
Or think about how much can be accomplished in 15 one-hour tutoring sessions
Commit to helping students visualize mathematics.
Daily review is one way to act on your compulsions and broaden the scope of any single lesson beyond a narrow focus on the day’s major objective.
Another way to view the 5 to 8 minutes allocated to this daily activity is to consider that 5 minutes x 180 days equal 900 minutes, or 15 hours! You know that you can change the world in 15 hours. Consider that 15 hours is about half a college course. Or think about how much can be accomplished in 15 one-hour tutoring sessions. It boggles the mind of many teachers and tutors that you can often cover much of an Algebra I course in 10 one-hour sessions and do it well. So in fact, these 5 minutes a day are roughly equivalent to half an hour per week of tutoring for an entire semester.

48. Mini-Math Reviews
Quick, focused, aligned with the curriculum, reflective of what is coming on assessments, and wonderfully informative.
What more could we ask from the first few minutes of a lesson?

49. Now, your turn…
With someone in your grade level, create your own mini-math questions.
1. review addition/subtraction situations
2. place value concept
3. Mentally adding/subtracting 10/100
4. geometry/shapes/arrays
5. measurement

50. In Summary
A deliberate and carefully planned support for ongoing, cumulative review of key skills and concepts
Using cumulative review to keep skills and understanding fresh, reinforce previously taught material, and give students a chance to clarify their understandings
The use of a brief review and whole-class checking of “mini-math: questions as an opportunity to re-teach when necessary

51. No more ineffective …

52. Accessible Mathematics: 10 Instructional Shifts That Raise Student Achievement Steve Leinwand
© 2012 Karen A. Blase and Dean L. Fixsen

53. What questions do you have?

54. Let’s play some games!
Choose a game to play.

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59. DPI Mathematics Section
Kitty Rutherford
Elementary Mathematics Consultant
Denise Schulz
Johannah Maynor
Secondary Mathematics Consultant
Lisa Ashe
Dr. Jennifer Curtis
K – 12 Mathematics Section Chief
Susan Hart
Mathematics Program Assistant 59

60. For all you do for our students!