Math Counts!K-3 Concepts

March 23, 2016

Session Goals:

● Develop a familiarity with some math strategies being used in K-3 classrooms● Discover some activities that support math learning at home

Consider This:

● Who remembers: Ours is not to reason why; just invert and multiply!● A student’s job in math class is to reason, and a teacher’s job is to help students

see that math makes sense. ● Mastery = Deep Understanding + Fluency + Application

Overview

Warm-Up ExerciseRoutines for Counting:

● Count on by ones from a given whole number● Count back by ones from a given whole number● Skip count on or back from a given whole number

(10s, 5s, 2s, 100s, etc.)● Count on or back by a fraction from a given number● Count on or back by a decimal from a given number

Communicating Positive Math MessagesParent Messages

“You can do it!”“Try another way”“What do you know?”“What strategy can you use?”“Have you seen something like this before?”“How can you get started?”

Encourage Positive Self-Talk

Instead of, “I’m not good at this,”Try, “I can be good at this, but I have to try!”

Instead of, “This is too hard,”Try ,”It might take some time and practice, but I can do this!”

“I was never good at math either.”

What is Number Sense?Integration of:

● number concept○ identification of numbers

○ counting

○ relative magnitude

○ relationships

○ decomposition/recomposition

● sight facts● place value understanding

Counting as the Foundation for All Math Concepts

Counting allows students to

experience patterns, sequence,

and conserve number

K - Counting StrategiesEnd of year expectations: Students will count to 100 by 1s, 2s, 10s from any number

Strategies:

● Counting forward from a given number in the sequence

● Exploring pattern

Activities for At-Home Practice:

● Daily counting, pick a “number of the day”, purposeful counting

Gr. 1 - Counting StrategiesEnd of year expectations - Students will count forward and back to 120 from any number

Strategies:

● Using Number Patterns ● Skip counting by 2s, 5s, and 10s

Activities for At-Home Practice:

● Daily counting● “What’s Next” game

What is Fact Fluency?● Knowing sums of 1-digit numbers

○ with understanding

○ with speed

○ with accuracy

Students who are “fluent” are both quick and efficient. They are able to recall information effortlessly, without constructing it.

Fact Fluency is not

memorization

K - Fact Fluency to 5End of year expectations - Students will fluently add and subtract within 5. Compose and decompose 1-digit numbers (1 - 9) to make ten.

Strategies:

● Subitize● Make 10

Activities for At-Home Practice:

● Bingo games● Go Fish for Ten

Gr. 1 - Fact Fluency to 10End of year expectations - Students will be fluent with addition and subtraction facts within 10

Strategies:

● Compose/Decompose ● +/- 1 , 2, doubles, near doubles

Activities for At-Home Practice:

● Cuisenaire Rods● Dice and card games

Importance of Fact Fluency● Use in multi-digit addition and

subtraction problems● Composing/decomposing

numbers help with mental math

38 + 46 = 38 + 2 + 44

● Students who lack fluency use

more Working Memory than those who are fact fluent

Gr. 2 Fact FluencyEnd of year expectations - Students will be fluent with all sums of two 1-digit numbers and their related subtraction facts

Strategies:

● Fact families - relationship between numbers

● Cuisenaire rods - colorful, different length manipulatives

● Learn in sequence - build upon each other and number sense

Gr. 3 Fact FluencyEnd of year expectations - Students will be fluent with all products of two 1-digit numbers and their related division facts

Strategies:

● Equal Groups of (3 x 5 = 3 groups of 5 = 15)

● Repeated addition (3 x 5 = 5 + 5 + 5 = 15)

● Arrays (3 x 5 = 3 rows with 5 in each = 15)

● Area model - Rectangle with length of 5 and width of 3 (Area = L x W )

Activities you can use at home!● ORAL FACTS - anytime - anywhere

○ - in the car, in the store, on a walk

● The best kind of FLASH CARDS (1+1 through 9+9) and (1x1 through 9x9)○ Two piles - Ones I know, Ones to Learn

○ Sequence of learning is important

● CUISENAIRE RODS - make all sums up to ten, say each fact 4 ways

● Computer applications - FasttMath, SumDog, Sushi Monster, ABCya

● Traditional Games - Addition Top-It, Math Fact Concentration

Food For Thought“As we expect every child to read fluently with comprehension by the end of third grade, we should expect and work for every child to have mastery of numeracy with understanding by the end of fourth grade so that they can learn mathematics easily, effectively, and efficiently and appreciate its reach, power, and beauty.”

~ Professor Mahesh Sharma, Mathematics For All

MathCounts!