BUILDING NUMBER SENSE THROUGH MAPPING DEVICES - KINDERGARTEN

K-2 CCSS MNPS District TrainingJune 10 – 14, 2013

Kari McLaughlin, Tameka Gordon-Sneed & Keri Davis, Jill Baker – District Numeracy Coaches

Building Number Sense is Essential for Student Learning Number sense refers to a person’s general understanding

of number and operations and the ability to handle daily life situations that include numbers. This includes the ability to develop useful, flexible and efficient strategies (i.e. mental computation) for handling numerical problems. - Howden, 1989; McIntosh, Reys & Reys 1992, etc.

Students who participate in well-designed activities are more likely to develop number sense than students who receive instruction focusing on the development of standard written algorithms and computation proficiency.

- Sowder, 1941; Reys 2001 In this session, we will look at instruction that is fostering

number sense.

Early Numeracy Strategies Developing spatial relationships involving hands-on

experiences (i.e. provide sensory input that helps students develop mental imagery)

Focusing on the meaning of sets in the context of problems

Developing visual cues such as dot cards and patterns on the die help students see relationships.

Building mental imagery expands children’s ability to think in flexible ways.

Recording students’ ideas as they share them can reinforce concepts and help students make the connection between the concrete items and the abstract numbers.

Early Numeracy Strategies Solving problems involving joining, separating,

grouping, and sharing helps students see how sets come together and are taken apart.

Counting and showing objects to 120 helps students to hear the number pattern and see quantities.

Counting forward and backward Ordering/sequencing sets, pictures, and numbers from

least to greatest Matching numerals to objects Being exposed to part/whole relationships Showing students sets and asking them to make

estimations of the quantities.

Numeracy Activities – Mapping Devices

Subitizing – Pattern recognition Ten Frame Recognition (Math Racks) Part-Part Whole Number Line (Number Paths) Number Chart

Subitizing Definition: “Instantly seeing how many”; It

is a prerequisite to basic math skills. It is the ability to look at a number pattern and instantly recognize that number without counting. Ability to recognize dot arrangements in different patterns. (Douglass, 1925)

Where do we use our knowledge of grouping and patterns in real- world situations?

Subitizing (cont.) Links to subitizing slide shows (dice, dominoes, five

frame, ten frames) Let’s practice! www.ircsd.org/webpages/dyoung/subitizing.cfm

Together let’s brainstorm questions we can ask students to advance their thinking

What content and practice standards are met by subitizing?

Five & Ten Frames Five Frames –

Counting, Combinations (Decompose, Compose)

http://illuminations.nctm.org/ActivityDetail.aspx?ID=74

Why are we building sense of 5?

Ten Frames Ten Frames –

How many, how many more, build, add, subtract

http://illuminations.nctm.org/ActivityDetail.aspx?ID=75

Why we are building sense of 10? Sample 5 & 10 Frame Games – Fish,

Memory, War

Math Racks What is a Math Rack? The original arithmetic rack, also known as a Rekenrek, was

developed by Adrian Treffers, a mathematic curriculum researcher, at the Freudenthal Institute in Holland.  It was designed to support the natural mathematical development of children’s addition and subtraction strategies as well as encourage and enhance children’s strategic mathematical thinking.

Though it resembles an abacus it is not based on place value columns and it is not used in that way.  It is comprised of two rows of tens, each broken into two sets of five.  This allows the children to ‘privilege 5’ and ‘think 10’ which leads to better number sense, efficient calculation and quick recall of math facts.

 

Math Racks Let’s create a Math Rack! How can the math rack be used to teach

Sets/Groups to 5Sums to 10Skip counting 2, 5, and 10

Greater than/less than Let’s take a look at some other types of math racks

and strategies? www.mathrack.com What content and practice standards are met

by ten frames and math racks?

Part-Part-WholeFrom Part-Part-Whole Exploration: Finger PPW Aural Representations Bunny Ears Hidden Hands PPW (in pairs)

Part-Part-WholePart Part Whole Unknown Cards

http://web.sd71.bc.ca/math/uploads/lessons_activities/grade1/Number/ppwcards.pdf

Part-Part-Whole

What content and practice standards are met by using the part-part-whole relationships?

Number Line (Number Paths)Counting builds to a mental visualization of a number line

K

K-1 use of number paths.

Number PathsWhy use the Number Path/Number Line?

CountingAdditionSubtractionGrouping of Sets

Show 6 + 3 on your MathRack

• Write down an equation that represents how you determine the total number of beads shown

• What relationships did you use?

• Model what you did on your Number Path

5 + 1 + 3

6 + 3

3 + 3 + 3

6 + 3 = 9

Show 9 - 6 on your MathRack

• Write down an equation that represents how you determine the total number of beads left

• What relationships did you use?

• Model what you did on your Number Path

9 - 6

What content and practice standards are met by using the number path/number line?

Number Chart

0-99 chart vs.100 chart

What do you think?

What portion of the charts is most appropriate for noticing patterns in Kindergarten?

*only exception is skip counting by 10s*

“What’s my number?” Give students clues for a number and

have them use the number chart to figure it out.

Examples:My number is less than 5. What could my number be?My number is 3 more than 2. What’s my number?

Wonders of the Number Chart

Activity 1: Special Numbers Have students place five to ten counters on their very special numbers. Have students tell a partner why these numbers are important to them. Examples of special numbers may include: Your age The day you were born The number of people in your familyThe number of pets you have

Activity 5: Number Patterns Have students begin by covering all numbers that have a 2 in either the ones place. Have students discuss the patterns or number relationships they observe. Repeat with other patterns.

What content and practice standards are met by using number charts?

How will you build number sense in your classroom?

Questions?