Improving Mathematical Understanding

Deepening Number Sense

Quantity

Symbol

Verbal

How do kids represent number?

• Level 0- Subitizing numbers up to 3, raises fingers sequentially.• Level 1- Subitizing regular patterns up to 6 and

irregular patterns up to 5, raises fingers simultaneously up to 5.• Level 2- Recognize 5-wise and pair-wise

structures, create finger patterns, combine and partition numbers up to 10.

• Level 3- Uses the sub-base of 5 to combine and partition numbers up to 10 without

counting.• Level 4- Combines and partitions numbers up to

20 using 10-plus and doubles.• Level 5- Uses sub-base of 5, base of 10, and

doubles to combine and partition numbers up to 20 without counting.

81 – 79 =

11 – 8 =

Number Sense vs. Teaching the Standard

Algorithm

7981

811

Fact Fluency

Number Line

13 14 15 16 17 18 19 20

Open Number Line

Ten Frames

Dot CardsSubitizing

Task 1Flashed Dot Patterns

What interventions should we do to support this?

Task 2Finger patterns

What interventions should we do to support this?

1 2 3 4 5 6 7 8

It is important to know what type of thinkers your students are. Interval thinkers like the number line. Discrete thinkers don’t understand the number line. They need concrete objects.

Interval Thinkers think in terms of jumping on the number line.Example: 12 remove 3I have 12 so 11, 10, 9-I have 9 left. (12…. 11, 10, 9)

1 2 3 4 5 6 7 8 9 10 11 12 13

1110 9

I have 9 left.

Discrete Thinkers think in terms of counting individual objects.Example: 12 remove 3I removed 12, 11, and 10 so I have 9 left. (12, 11, 10……9)

Johnny had 12 heart cookies. He gave his friend Mr. 12, Mr. 11, and Mr. 10, so he had 9 left.

1211 10 I have 9

left.

Task 3Name and visualize

quantities on a pair-wise ten frame

What interventions should we do to support this?

What does the Investigations

curriculum do to develop number

sense?

What are your next steps?