1. Examples
Sybilla Beckmann
Department of Mathematics, University of Georgia
STEM Summit 2010
Sybilla Beckmann (UGA) Examples 1 / 12

2. What is there to know about counting?
If a child can correctly say the first five counting numbers,
“one, two, three, four, five,”
will the child necessarily be able to determine how many blocks there
are in this collection?
Why or why not?
Sybilla Beckmann (UGA) Examples 2 / 12

3. What is there to know about counting?
Child 1: Child 2:
“1” “2” “3” “4” “1” “2” “3” “4”
Child 3: Child 4:
“1” “2” “3”“4” “5” “6” “1” “2” “3”“4” “5” “6”
Sybilla Beckmann (UGA) Examples 3 / 12

4. What is there to know about counting?
Teacher: “How many blocks are there?”
Child 1: Child 2:
“1” “2” “3” “4” “5” “1” “2” “3” “4” “5”
Teacher: “So how many blocks are there?”
Child 1: Child 2: “Five all
together!”
“1” Sybilla Beckmann (UGA) “4”
“2” “3” “5” Examples 4 / 12

5. Building connections
Math is connected across grade levels and across topics
A common spirit and approach can connect math and the sciences:
inquiry
expecting ideas to make sense
engagement, exploration, and playfulness
Sybilla Beckmann (UGA) Examples 5 / 12

6. Early math connects to later math
Young children make pictures and designs with pattern tiles
Sybilla Beckmann (UGA) Examples 6 / 12

7. Early math connects to later math
Young children can compose and decompose shapes to make new
shapes
Sybilla Beckmann (UGA) Examples 7 / 12

8. Early math connects to later math
Grouping to create a new unit
10 ones are grouped
to form one ten
Sybilla Beckmann (UGA) Examples 8 / 12

9. Early math connects to later math
Determining areas
6 cm
What is the 3 cm
6 cm
area of the shaded 7 cm
shape?
4 cm
12 cm
Method 1 Method 2 Method 3
7×6 + 4×6 3×6 + 4×12 7×12 - 3×6
Sybilla Beckmann (UGA) Examples 9 / 12

10. Early math connects to later math
Understanding the common multiplication algorithm
10 + 4
14
×13
10 10×10 10×4 12
30
40
+ 100
3 3×10 3×4
182
Sybilla Beckmann (UGA) Examples 10 / 12

11. Early math connects to later math
Understanding the triangle area formula
One method:
h
b
h
b÷2
Sybilla Beckmann (UGA) Examples 11 / 12

12. Early math connects to later math
Understanding the triangle area formula
Another method:
h h
b b
h
b
Sybilla Beckmann (UGA) Examples 12 / 12

13. Early math connects to later math
Calculus
y
1
y = x2
dx 1 x
1 1
1 3 1
area under curve = x 2 dx = x =
0 3 0 3
Sybilla Beckmann (UGA) Examples 13 / 12