Teaching to the Next Generation Sunshine State Standards. August 17, 2010. Next Generation Sunshine State Standards. Eliminates: Mile wide, inch deep curriculum Constant repetition Emphasizes: Automatic Recall of basic facts Computational fluency
August 17, 2010
Low ComplexityRelies heavily on the recall and recognition; computation
Moderate ComplexityInvolves flexible thinking and usually multiple operations; problem solving
Requires more abstract reasoning, planning, analysis, judgment, and creative thought; multiple representations
Daily Spiral Review: Problem of Day
Interactive Learning: Purpose, Prior Knowledge
Visual Learning: Vocabulary, Instruction, Practice
Close, Assess, Differentiate: Centers, HW
Examples by grade level, Model drawing
Reasoning and Proof
Examples and counterexamples
Examples by grade level
Read, write, listen, think, and communicate/discuss
Tool for understanding and explaining
Increased use of math vocabulary
Examples of rich problems by grade level
Equivalence: fraction/decimal, cm/m
Other content areas, science
Real World contexts
The importance of developing number sense in a gradual sequence
Activities that build upon one another for students to gain a better sense of number relationships
Counting, which involves the skills of orally reciting numerals, matching and writing numerals to identify the quantity and understanding the concepts of more than, less than and equal to
NCTM Math Process Standards:
Reasoning and Proof
Cooperative learning, emergent literacy instruction, the use of manipulative materials, and think-pair-share will be highlighted
Represent quantities with numbers
up to 20, verbally, in writing, and
with manipulatives. (Moderate)
Model addition and subtraction situations using the concepts of “part-whole”, “adding to,” “taking away from”, “comparing,” and “missing addend”. (Moderate)
Recall basic addition and related subtraction facts. (Low)
Identify relationships between the digits and their place values through the thousands, including counting by tens and hundreds. (Moderate)
Write down the last two digits of the year you were born. (A)
Divide that number by 4 and ignore any remainder. (B)
Write down the day of the month you were born. (C)
Add A + B + C + D
Divide this total by seven and use the Table. (D)remainder to see which day you were born on from the table
Inclusion-If you ask a child to bring you 5 toy trucks and he brings you the fifth truck that he counts, he may not understand that all 5 trucks are included in the entire set of trucks. The fifth truck is only part of the set.
One-to-One Correspondence -The matching of one number to one object. Children who call numbers at a faster or slower rate than they are able to point to, may not yet have mastered the skill.
Conservation of Number Table. (D) -Children have acquired conservation of number when, for example, they recognize that a group of objects clustered tightly together still contains the same number of objects when spread over a larger area.
Number Sense and Relationships - Just like learning to read, learning to count requires numerous opportunities for purposeful counting.Foundational Number Concepts
Table Talk Activity: Table. (D)
What do you know about five?
The answer is 5, what is the question?Give Me Five!
Write the number 1 on an index card
Place the card on the table
Place one counter above the card
Write another number card that is one more than the first number
Place the appropriate number of counters above that card
Continue until you have sets of 1-5
Read the article, “ Developing ‘Five-ness’ in Kindergarten” and highlight the meaningful points.
Discuss highlighted points with table partners.
Compare learning experiences identified in the article, with your past instructional strategies.
How does the depth of knowledge in the ‘Five-ness” activities compare to the ‘Day of the Week” activity?
Create a picture using up to 5 colors.
Complete the sentence below and write it on the bottom of the picture.
I used _______different colors in my picture.
Sally has 4 apples. Jimmy has the same. How many apples does Jimmy have?
Sally has 4 apples. She has 3 more than Jimmy. How many does Jimmy have now?
Dot Cards 1-5
Shuffle the cards and give a set to each group.
One person takes a card, the others find a card that is fewer or more than.
Repeat so every one gets a turn.
The standard for mathematics should be the same as the standard for reading-bringing meaning to the printed symbols. In both situations, skills and understanding must go hand in hand. The challenge is how do we help students develop meaning and make sense of what they do?”
Discuss Marilyn Burns’ purpose in the statement above.
Why Connect Mathematics and Literature?
Mathematics and literature bring order to the world around us
Math and literature classify objects
Math and literature emphasize problem solving skills
Math and literature involve relationships and patterns
Read the text aloud
Draw a number line on chart paper sequenced from 0 to 10
Place the appropriate amount of sticky dots above the line to represent each counting number
Count the number of sticky dots above each number
Find a partner from another group
Count the number of dots together
Explain how your books are similar and different
In what ways might you revise current instructional strategies to incorporate the in-depth understanding intendedby the Next Generation Sunshine State Standards?
Show me 4 objects on the 10 frame.
How many counters are on the 10 frame?
Show me 2 more, what is the number now?
How many more to make 10?
Show me seven.
Show me 1 more, what is the number now?
Show me 2 less, what is the number now?
How many more to make 10?
Using 2 ten frames, show me 13.
Show me 5 more, what is the number now?
Show me 6 less, what is the number now/
How can you make 20?
How does the depth of knowledge in the “Show Me” activity compare to the “Five-ness” activity?
How are the process standards of problem solving, representation, communication, reasoning and proof, and connections addressed in the previous activities?
How will allowing students to think for themselves impact their computational fluency?
Looking back at the benchmarks discussed, what background knowledge must children know in order to meet the requirements of this standard?
How might you utilize manipulatives to support conceptual depth and understanding?
How will you assess students’ understanding of the benchmark, MA.K.A.1.1?
What other benchmarks in grades K-2, are related to this benchmark?
In what ways might you revise current instructional strategies to incorporate the in-depth understanding intended by the Next Generation Sunshine State Standards?
Participants will explore …
The use of invented strategies to solve multi-digit addition and subtraction problems
The use of Base 10 blocks, partial sums, and differences to solve multi-digit addition problems
The empty number line as a method to focus on place value when solving subtraction problems
These strategies are personal and flexible for the students
Students will solve the same problem in different ways that make sense to them
“There is mounting evidence that children both in and out of school can construct methods for adding and subtracting multi-digit numbers without explicit instruction.” (Carpenter, et al., 1998, p. 4)
You’re not allowed to use it today
The two scout troops went on a field trip. There were 46 girl scouts and 38 boy scouts. How many scouts went on the trip?
Van de Walle, 2007, p. 223
Sam had 46 baseball cards. He went to a card show and got some more cards for his collection. Now he has 73 cards. How many cards did Sam buy at the card show?
Van de Walle, 2007, p. 223
There were 84 children on the playground. The 37 second-grade students came in first. How many children were still outside?
Van de Walle, 2007 p. 225
Tommy was on page 67 of his book. Then he read 58 more pages. How many pages did Tommy read in all?
Van de Walle, 2007, p. 222
What are the advantages of using invented strategies?
What are the disadvantages of using invented strategies?
What depth of knowledge does this activity lead to?
Utilize word problems
-Notice the wording involved in the previous problems
Allow plenty of time
Listen to different strategies
Have students explain their methods
Record verbal explanations for others to
Pose problems to be solved mentally
Using Base -10 Blocks for Addition
For each problem, one person of the pair should be the “doer” and the other person the “recorder.”
Keep a “written record” to translate what you do with the blocks into a paper-and-pencil algorithm.
Problem 1: 27 + 58
32 + 29 = (30 + 2) + (20 + 9) = (2 + 9) + (30 +20) = 11 + 50 = 61
32 + 29 = (30 + 2) + (20 + 9) = (2 + 9) + (30 + 20) = 11 + 50 = 61
Using Base-10 blocks and place-value charts to develop the traditional algorithm for subtraction.
73 – 26 = (70 + 3) – (20 + 6) = (60 + 13) – (20 + 6)= (60 – 20) + (13 – 6)= 40 + 7 = 47
Divide into dyads
Read your half of the article (5 min.)
Highlight important ideas
When ready, share your ideas with your partner
What was surprising or interesting within your group discussion?
Be ready to describe the child’s strategy to your partner
What depth of knowledge is exhibited in this strategy?
Examine the Big Ideas related to the Base-10 Number system across Grades K - 2.
How might you use the strategies/methods discussed today in your classroom?
What do you expect your students to find challenging about invented and standard methods for addition and subtraction?
What misconceptions might students hold about addition and subtraction that you will need to address?