Kindergarten Math Morning
Heather Zetterberg
Math Specialist, Grades K-9
Learning Basic Math Facts How Does It Feel?
Count on the Alphabet to Find Out
What Are Basic Facts?
● Basic math facts are defined as computations involving the four basic math operations using the numbers 0 – 10.
● These basic facts are also referred to as “basic number combinations”
For example:
Step Into Your Child’s Shoes
● Experience what your child might feel as they begin to learn strategies for recalling basic math facts and solving arithmetic problems.
● Get a snapshot of how and why Foote teachers teach basic facts.
Adults…
● Have developed a familiarity with the number sequence
● Have a good sense of number and are able to manipulate numbers
● Might have difficulty remembering what it was like when we were beginning to learn our basic facts
Young Children…
● Need time and many opportunities to develop a conceptual sense of number even though they are proficient reciting the number sequence
● Don’t necessarily have a sense of how big a number is or what it represents
● Children in Kindergarten are capable of counting to twenty and beyond.
● Knowing the counting sequence is critical to being able to add and subtract.
1 + 3 =
4 + 4 =
5 + 6 =
9 + 7 =
This morning…
● We will use the letter symbols to represent quantities.
● The letters A, B, C, D, E, F, G, H, and I are the symbols we will use to keep track of quantities.
● The symbol # will represent zero.
For Example…
For Example… = B
For Example… = B
For Example… = B
Let’s Try Another
Let’s Try Another
Let’s Try Another
Let’s Try Another
Why Letters?
● We all know the alphabet sequence.
● We all know the “relative magnitude” of letters.
➔ We can put words in alphabetical order.
● However, we may not have mastered the quantity that each letter represents.
There Are Two Important Rules for This Morning
1. You are NOT permitted to translate letters to numbers! = B, not 2!
There Are Two Important Rules for This Morning
2. You may NOT make a table or chart or cheat sheet of any form that shows: A = 1 B = 2 C = 3 etc…
However, you have access to two tools
A Letter Line and a Letter Chart are available on page 2 of your handouts.
Keep a mental record of any strategies you use while you work on answering problems you will be given.
Let’s Do a Little Warm Up
A+ C =
A + C = D
D + D =
D + D = H
E + F =
E + F = AA
G + I = AF
Your Turn To Try
● Turn to page 3 of your handout packet.
● Answer the problems as efficiently as you can. Take about 2 minutes to complete as many of the facts as you can.
● You may work with someone, but please do not copy anyone’s answers.
How Did That Feel?
● Did that experience spark any memories of your time in elementary school?
● Did you use any tools, manipulatives, or strategies to help find the answers?
Why
is
Basic Fact Fluency Important?
● Fact fluency contributes to a child’s ability to solve more difficult problems more accurately and more efficiently.
● When fluent, students free up their working memory and can devote it to problem-solving and learning new concepts and skills.
Why is Basic Fact Fluency Important?
● When students have fact fluency, they are better able to learn algorithms.
● Fact fluency allows students to manage mental computations, estimate solutions, and determine the reasonableness of answers more effectively.
Four Fundamentals of Fact Fluency
1. Mastery must focus on fluency
Computational Fluency
Four Fundamentals of Fact Fluency
1. Mastery must focus on fluency
2. Fluency develops in four phases
Fluency Develops in Four Phases
1. Direct-Modeling
• Physical objects are used to represent both of the quantities
• Both quantities are joined together then the whole collection of objects is counted
Fluency Develops in Four Phases
2. Counting
• One of the quantities is generated or kept in mind
• The other quantity is “counted on” using objects or fingers
Finger Use and Fact Recall
● Research shows there is a strong correlation between finger perception and the development of number sense
● Numerical representations appear to be rooted in early sensorimotor experiences of finger use like counting and calculating
● Blind children use their fingers for counting and displaying quantities
Finger Use and Fact Recall
● “Finger-based strategies constitute a natural scaffold for the development of crucial numerical abilities and may be highly advantageous for most – if not for all –children in early stages of their numerical development.” Barrocas et al 2020
● “FMS (fine motor skills) are closely related to early numerical skill development through finger-based numerical counting that aids the acquisition of mathematical mental representations.” Fischer, Stoeger, Suggate. 2017
Fluency Develops in Four Phases
3. Derived Fact
• Certain facts are known
• These facts are used as springboards for other, related facts
Fluency Develops in Four Phases
4. Mastery
• Answers are efficiently produced
• Facts are answered within 3 seconds by quick strategy application or recall
Four Fundamentals of Fact Fluency
1. Mastery must focus on fluency
2. Fluency develops in four phases
3. Foundational facts must precede derived facts
Addition Fact Progression
Sequence of Basic Addition Fact Strategy Instruction
1. + 0
2. + 1
3. Counting On (+ 2)
4. Doubles (5 + 5)
5. Near Doubles: Doubles + 1 (5 + 6)
Two-Aparts (5 + 7)
Sequence of Basic Addition Fact Strategy Instruction
6. Pairs to Make Ten
7. Number Bonds
8. + 10
9. Make a Ten with 9
10. Make a Ten with 8
…Then there are the “leftovers”
The “Leftovers”
3 + 6
6 + 3 4 + 7 7 + 4
An Important Point
● Lack of basic math fact mastery is not a barrier to other good, rich math instruction and experiences.
Four Fundamentals of Fact Fluency
1. Mastery must focus on fluency
2. Fluency develops in four phases
3. Foundational facts must precede derived facts
4. Students need substantial and enjoyable practice
