Upload
roland-rogers
View
220
Download
0
Tags:
Embed Size (px)
Citation preview
THE NUMBERS 1 THROUGH 9 ARE PLACED ALONG THE SIDES OF THE FOLLOWING TRIANGLE SO THAT EACH SIDE HAS THE SAME SUM. HOWEVER, THREE OF THE NINE NUMBERS ARE COVERED. WHAT NUMBER IS IN THE CIRCLE WITH THE QUESTION MARK? WHY?
FIVE TOWER GAME
You NeedA partner Interlocking CubesTwo Dice
DirectionsRoll the dice and take that many cubes. Snap them in a
tower. Take turns doing this until you each have five towers.
Each of you now figures out how many cubes you have. Compare your counts. See if on of you has more than the
other or if you both have the same number of cubes. Marilyn Burns About Teaching Mathematics
AS WE USE SPECIFIC STRATEGIES TODAY WE WILL RECORD THEM ON CHART PAPER
Addition Strategies Subtraction Strategies
MASTERY OF BASIC FACTS
Phase 1 Counting Counts with objectsPhase 2 Deriving Uses reasoning strategies
based on known factsPhase 3 Mastery Efficient production of
answer
Adapted from Jennifer M. Bay-Williams and Giana King“Enriching Addition and Subtraction Fact Mastery Through Games”, 2014
PROGRESSING THROUGH THE PHASES IN THE STANDARDS
Pre-K and Kindergarten Represent addition and subtraction with object, fingers,
mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations (K.OA.1)
Grade 1 Add and subtract within 20, demonstrating fluency for
addition and subtraction within 10. Use strategies such as counting on; making ten; decomposing a number leading to a ten; using the relationship between addition and subtraction; and creating equivalent but easier or known sums. (1.OA.6)
Grade 2 Standard 2.OA.B.2 states, “Fluently add and subtract
within 20 using mental strategies. By end of grade 2, know from memory all sums of two one-digit numbers.” (CCSS, 2.OA.B.2)
FLUENCY
The Common Core State Standards for Mathematics (CCSS-M) describes procedural fluency as “skill in carrying out procedures flexibly, accurately, efficiently and appropriately.”
(CCSSO, 2010, p. 6)
HOW CAN TEACHERS ENSURE THAT THEIR STUDENTS ACQUIRE THE STRATEGIES NEEDED TO MASTER PHASE 2?
Explicitly teaching Strategies
EXPLICITLY TEACHING STRATEGIES
Does not mean teaching a specific strategy and then asking students to use it. Such an approach removes the reasoning from the reasoning strategy and instead adds to what a student is being asked to memorize.
EXPLICITLY TEACHING STRATEGIES
Means supporting student thinking, including asking students which strategy they might use in a given situation. The key is to help students see the possibilities and then let them choose strategies that help them get to the solution without counting
Focus on SMP 3
HIGH ROLLER
Players take turns, each time rolling two regular dot dice. After the first player rolls his two dice, he determines which on has the greater number (the high roller) and keeps that die as it is while rolling the other die a second time. He then counts on from the first die to get the sum of the two dice and records the sum. The second player repeats the process, and play continues as time allows.
NUMBER FRAMES
Go to http://www.mathlearningcenter.org/
Go to ResourcesGo to Free AppsClick on number frames web
CREATE YOUR OWN NUMBER TALK STRING
Create your own string of number talks using number frames and the online app to encourage the use of one of the following strategies for addition. Be prepared to share.
Commutative PropertyCombinations of 5, 10 or 100Decomposing or Composing NumbersDoubles plus one, plus two
NUMBER PIECES AND NUMBER RACK
Go to http://www.mathlearningcenter.org/
Go to Resources Go to Free Apps Click on number pieces web or the
number rack app link
TASK – SOLVE USING AS MANY STRATEGIES AND/OR TOOLS AS YOU CAN
There are crayons in a box. There are 4 green crayons, 5 blue crayons, and 6 red crayons. How many crayons are in the box?
Explain to others, how you found your answer.
CA Math Framework 1st grade Page 16
5 PRACTICES FOR ORCHESTRATING PRODUCTIVE MATHEMATICS DISCUSSIONS
1. Anticipating likely student responses to challenging mathematical tasks
2. Monitoring students’ actual responses to the tasks (while students work on the tasks in pairs or small groups)
3. Selecting the student responses that will be displayed in a specific order
4. Sequencing particular students to present their mathematical work during the whole-class discussion
5. Connecting different students’ responses and connecting the responses to key mathematical ideas
5 Practices for Orchestrating Productive Mathematics Discussion by Margaret S. Smith and Mary Kay Stein
TASK – WORK TOGETHER TO ANTICIPATE STUDENT SOLUTIONS
Some students are in the cafeteria. Twenty-four (24) more students came in. Now there are 60 students in the cafeteria. How many students were in the cafeteria to start with?
Use drawings and equations to show your thinking.
CA Math Framework 2nd grade Page 10
TEN FLASHING FIRE FLIES
How many different ways could 10 fireflies be arranged with some in the jar and some in the night sky?
WHAT STRATEGIES CAN YOU USE TO SOLVE EACH OF THESE? WHAT TOOLS CAN YOU USE TO HELP
YOU SOLVE THE PROBLEMS
96 + 9321-117
MEANINGFUL PRACTICE – MOVING TO PHASE 3
“Practice that follow substantial initial experiences that support understanding and emphasize ‘thinking strategies’ has been shown to improve student achievement with single-digit calculations.” (NRC, 2001).
MEANINGFUL PRACTICE
Games:Are engagingProvide opportunities for strategy
discussion and assessmentShould be sequenced developmentally
(for example, paying combinations of ten games before exploring making ten strategies.)
Can be targeted practice or general practice.
Lend to differentiation
SHAKE AND SPILL
Materials 5 two – color counters Cup
Directions Put the counters in the cup, shake it, and spill
them onto a table Determine how many of each color is showing Record the sum by using drawings or equations “Shake and Spill” several times to show different
pairs of numbers that sum to 5.
SALUTE!
From Kentucky Center for Mathematics, Kentucky Numeracy Project Intervention Guide
www.kymath.org