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?

ADDITION AND SUBTRACTION STRATEGIES

Grades TK-2 Summer Conference 2015

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

AGENDA

• 3 Phases of Basic Fact Mastery• Number Talks• Math Tasks• Games • Math Apps

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 TALKS

NUMBER TALKS    

       

    

       

    

       

    

       

NUMBER TALKS    

       

    

       

    

       

    

       

NUMBER TALKS    

       

    

       

    

       

    

       

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

BLOCKS BEHIND MY BACK

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

Number Bonds to Help Visualize Decomposing

Numbers4

59

9

4

5

9

96 + 9 = 105

4 5

HOW CAN YOU USE NUMBER BONDS, AND OPEN NUMBER LINES IN YOUR CURRICULUM?

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

REFLECTIONBelow record something “old” that you heard today and something “new” that you connected with. Record a question that you wish to research and learn more about.