1
U n t er r i ch t spl a n
Es t imat e Divis io n wit h De c imal s –
Two De c imal Pl ac e s
Altersgruppe: 5 t h Gr ade , 6t h Gr ade
Virginia - Mathematics Standards of Learning (2009): 5 .5 a, 6.7
Virginia - Mathematics Standards of Learning (2016): 5 .5 .a, 5 .5 .b,
6.5 .c
Fairfax County Public Schools Program of Studies: 5 .5 .a.4 , 5 .5 .a.5 ,
6.7 .a.1, 6.7 .a.2
Online-Ressourcen: A B al l par k E st i mat e
Opening
T eacher
present s
St udent s
pract ice
Mat h
Pract ice
8
12
12
10
3
min
min
min
min
min
Closing
M at h Obj e c t i v e s
E x pe r i e nc e so l v i ng estimation problems.
P r ac t i c e estimating division with decimals.
L e ar n that there are different degrees of accuracy in
estimation.
De v e l o p the concept of estimation.
Copyright 2015 www.matific.com
2
Ope ni ng | 8 min
Display the following problems:
28.9 ÷ 5 =
79.12 ÷ 7 =
A sk : Without solving the problem, estimate the value of the
expression 28.9 ÷ 5. How did you determine your estimate?
A possible response: The value is approximately 6, because 30 is
close to, and above, 28.9 and 30 divided by 5 is 6. So, 28.9 ÷ 5 will
be just under 6.
A sk : What is your estimate for the value of the expression 79.12 ÷
7? How did you arrive at that estimate?
A possible response: the value is close to 11, because 77 is close
to, and below, 79.12 and 77 divided by 7 is 11. So, 79.12 7 is just
over 11.
Show the following problem:
176.94 ÷ 9.3 =
A sk : Is the value of the expression larger or smaller than 20? How
do you know?
The value is smaller than 20, because 180 is close to, and above,
176.94 and 9 is close to, but less than 9.3 Therefore, 180 ÷ 9 is
20. Now, if we increase the dividend and decreased the divisor,
we get a larger solution. So, the value is smaller than 20.
Emphasize that the quotient is higher if the divisor is smaller, and vice versa.
Explain that the closer the estimate is to the exact answer, or the narrower
the range,the more accurate the estimate.
Copyright 2015 www.matific.com
3
T e ac he r pr e se nt s M at h game : A B al l par k E st i mat e Di v i si o n: T w o De c i mal P l ac e s | 12 min
Using Preset mode, on the projector, present Matific ’s episode A B a llp a r k
E s t im a t e - Div is io n : T w o De c im a l Pla c e s to the class.
This episode allows students to practice the estimation of quotients, using
whole numbers and decimals (two decimal places). Estimate each quotient
by marking a range on a number line. The narrower the range, the higher your
score.
Display, for the class, the second question, in the presentation mode.
E x a m p le :
S ay: Please read the instructions at the bottom of the screen.
Students read the instructions.
A sk: Let’s estimate the value of the expression 53.45 ÷ 7. How do
we know?
A possible response: the value of the expression is approximately
7.5, because 53.45 is approximately the middle between 49 and
Copyright 2015 www.matific.com
4
56, and 49 divided by 7 is 7, as well as 56 divided by 7 is 8. So the
quotient is approximately the middle of 7 and 8.
A sk : Is the value of the expression closer to 7 or 8?
Answers may vary, but students should be encouraged to
recognize 53.46 is closer to 56 than to 49, so the value of the
expression is closer to 8.
Now we mark our estimate on the number line.
E x a m p le :
Show students the third question, in the presentation mode.
E x a m p le :
Copyright 2015 www.matific.com
5
S ay: Please read the instructions at the bottom of the screen.
Students can read the instruction.
S ay: Let’s estimate the value of the expression 6.31 ÷ 0.2.
A possible response: We will use upper and lower limits. Consider
that 6 is close to, and less than, 6.31, and 7 is close to, and
greater than, 6.31. Division by 0.2 is like multiplying by 5, so the
lower limit is 5 x 6, which is 30, and the upper limit is 5 x 7, which
is 35. Therefore, the value of the expression is between 30 and
35.
A sk : Is the value of the expression closer to 30 or to 35?
Answers may vary, but students should be encouraged to
recognize that 6.31 is closer to 6 than to 7, so the value of the
expression is closer to 30.
Copyright 2015 www.matific.com
6
S t ude nt s pr ac t i c e M at h game : A B al l par k E st i mat e Di v i si o n: T w o De c i mal P l ac e s | 12 min
Have students play A B a llp a r k E s t im a t e - Div is io n : T w o De c im a l
Pla c e s on their personal devices.
Circulate answering questions.
Ask students, especially the stronger ones, not to settle for less than
excellent accuracy.
M at h P r ac t i c e : E st i mat i ng Di v i si o n W o r kshe e t | 10 min
Discuss any challenges students faced while working individually.
Ask the class for responses relating to how they dealt with common issues
encountered by their classmates.
Display the following problems:
74.25 ÷ 3 =
30 ÷ 1.6 =
8.51 ÷ 0.25 =
154.98 ÷ 15 =
Have students work in pairs. Ask them to arrange the quotients from
smallest to greatest.
After pairs have worked for a few minutes, provide time to share.
A sk : What is your estimate for every quotient? How did you
determine your estimate?
The value of 74.25 ÷ 3 is between 24 and 25,because 75 is close to,
Copyright 2015 www.matific.com
7
but above, 74.25, and 75 3 is 25. Therefore, 72 is close to, and
below, 74.25, so 72 ÷ 3 is 24.
The value of 30 ÷ 1.6 is just under 20, and 1.5 is close to, and below,
1.6, therefore, 30 ÷ 1.5 is 20. So, if we increase the divisor we
decreased the quotient and 2 is above 1.6, we determine 30 ÷ 2 is
15. So, the range is from 15 to 20.
The value of 8.51 ÷ 0.25 is just over 34, because 8.5 is close to, and
below, 8.51. Division by a quarter is like multiplying by 4, with 4
times 8.5 equalling 34.
The value of 154.98 ÷ 15 is just over 10,since 150 is close to, and
below, 154.98. Consider 150 ÷ 15 is 10, and 165 is above 154.98,
therefore 165 ÷ 15 is 11. So, the range is between 10 and 11.
The correct sequence, from smallest to largest, is:
154.98 ÷ 15
30 ÷ 1.6
74.2 ÷ 3.2
8.51 ÷ 0.25
C l o si ng | 3 min
S ay : State each step needed to decide which value is lower: 9.25 ÷
3 or 9.1 ÷ 3.1.
9.25 is bigger than 9.1 and 3.1 is bigger than 3, therefore 9.1 ÷ 3.1
is lower than 9.25 ÷ 3, because the quotient is higher when the
divisor is smaller, and the quotient is higher when the dividend is
higher.
Copyright 2015 www.matific.com