Early DivisionEarly Division on MathLineon MathLine

Early Division

Early divisionEarly division includesincludes:

• Division as Repeated SubtractionDivision as Repeated Subtraction

• Breaking into Equal Groups orBreaking into Equal Groups or

Students think about Students think about Early Division Early Division

both ways!both ways!

Early Division

• Equal Groups DivisionEqual Groups Division

• Division as Repeated SubtractionDivision as Repeated Subtraction

• Computational DivisionComputational Division

• Division with RemaindersDivision with Remainders

Division on MathLineDivision on MathLine includesincludes::

• Long Division (single digit divisor) Long Division (single digit divisor)

Early Division

MathLine MathLine will effectively model will effectively model

ALL ALL aspects of division aspects of division for your students!for your students!

Early Division

This lesson covers This lesson covers

Early Division

• Equal Groups DivisionEqual Groups Division• Division as Repeated SubtractionDivision as Repeated Subtraction• Computational DivisionComputational Division

Equal Groups DivisionEqual Groups Division

Early Division

using ‘trial & error’using ‘trial & error’

If we have 18 cookies in a jar, If we have 18 cookies in a jar, and we put them into and we put them into

3 equal piles. 3 equal piles. How many in each pile?How many in each pile?

Early Division

Find 3 equal groups Find 3 equal groups

Early Division

Find 3 equal groups Find 3 equal groups of 18 using ‘trial & error’of 18 using ‘trial & error’

18 ÷18 ÷ 33

Early Division

Groups of 7?Groups of 7?

18 ÷18 ÷ 33

Early Division

1 2 3 4 5 6 7

Groups of 7?Groups of 7?

18 ÷18 ÷ 33

Early Division

1 2 3 4 5 6 7

Groups of 7?Groups of 7?

18 ÷ 18 ÷ 33

Early Division

1 2 3 4

NoNo

Groups of 7, 7 & 4 Groups of 7, 7 & 4 are not equalare not equal

18 ÷ 18 ÷ 33

Early Division

7 7 4

Groups of 6?Groups of 6?

18 ÷18 ÷ 33

Early Division

1 2 3 4 5 6

Groups of 6?Groups of 6?

18 ÷18 ÷ 33

Early Division

1 2 3 4 5 6

18 ÷18 ÷ 33

Early Division

1 2 3 4 5 6

Yes Yes Groups of 6?Groups of 6?

Early Division

18 ÷18 ÷ 33 = 6 = 6

See 18 divides by 6 - 3 times.See 18 divides by 6 - 3 times.So each pile has 6 cookies.So each pile has 6 cookies.

1 2 3

Division asDivision as Repeated Subtraction Repeated Subtraction

Early Division

If we have 24 students If we have 24 students playing soccer at gym time, playing soccer at gym time,

and they split up into teams of 6. and they split up into teams of 6. How many teams are there to How many teams are there to

play soccer?play soccer?

Early Division

Now divide by Now divide by subtracting subtracting

Early Division

Division as Division as repeated subtractionrepeated subtraction

One group of 6 from 24One group of 6 from 24

24 ÷ 6 = 24 ÷ 6 =

Early Division

123456

24 ÷ 6 = 24 ÷ 6 =

Early Division

Two groups of 6 from 24Two groups of 6 from 24

123456

24 ÷ 6 = 24 ÷ 6 =

Early Division

Three groups of 6 from 24Three groups of 6 from 24

123456

24 ÷ 6 = 24 ÷ 6 =

Early Division

Four groups of 6 from 24Four groups of 6 from 24

123456

24 ÷ 6 = 24 ÷ 6 = 44

Early Division

Answer is 4, Answer is 4, or there will be 4 teams or there will be 4 teams

to play soccer.to play soccer.

1 2 3 4

Computational division Computational division

Early Division

Typically done through Typically done through repeated subtraction repeated subtraction

22 ÷ 4 =22 ÷ 4 =

Early Division

22 ÷ 4 =22 ÷ 4 =

Early Division

1234

22 ÷ 4 =22 ÷ 4 =

Early Division

1234

22 ÷ 4 =22 ÷ 4 =

Early Division

1234

22 ÷ 4 =22 ÷ 4 =

Early Division

1234

22 ÷ 4 =22 ÷ 4 =

Early Division

1234

22 ÷ 4 = 22 ÷ 4 = 55

Early Division

12

5 groups of 4 5 groups of 4 With how many left over?With how many left over?

Early Division

12

With two left over, remainder of 2With two left over, remainder of 2

22 ÷ 4 =22 ÷ 4 = 5 r 25 r 2

Early Division

12

22 ÷ 4 =22 ÷ 4 = 5 r 25 r 2

Notice that remainder 2 Notice that remainder 2 is also 2 of 4is also 2 of 4

22 ÷ 4 =22 ÷ 4 = 5 r 25 r 2

Early Division

12

Equal to Equal to 2/42/4 or or 1/21/2

22 ÷ 4 =22 ÷ 4 = 5 r 1/25 r 1/2

Computational division Computational division

Early Division

also can divide also can divide from left to rightfrom left to right

Early Division

1 2 3 4

22 ÷ 4 =22 ÷ 4 =

Early Division

1 2 3 4

22 ÷ 4 =22 ÷ 4 =

Early Division

1 2 3 4

22 ÷ 4 =22 ÷ 4 =

Early Division

1 2 3 4

22 ÷ 4 =22 ÷ 4 =

Early Division

1 2 3 4

22 ÷ 4 =22 ÷ 4 =

22 ÷ 4 =22 ÷ 4 =

Early Division

1 2 3 4 5

5 groups of 4 5 groups of 4 With how many left over?With how many left over?

Early Division

With two left over, remainder of 2With two left over, remainder of 2

22 ÷ 4 =22 ÷ 4 = 5 r 25 r 2

1 2