Lesson Plan
Topic:
Estimating & Finding Exact Quotients
Time Allotted: 1.5 hours
Grade/Subject: 6
Unit:
Outcomes
1.
Students will estimate quotients.
2. Students will find exact quotients.
Assessment of outcomes/objectives:
Materials
1. Students are able to estimate quotients (determined by
observation).
Paper & pencil
2. Students are able to determine exact quotients (determined
by observation).
Introduction/Anticipatory Set:
Introduction- What is 45 ÷ 9? What multiplication could help find this quotient? What is 28 ÷ 7? What
multiplication is related to this division fact?
Estimate 75 ÷ 8 is about _____. What multiplication could help you find a close estimate? 8 x ___ is
close to 75? 8 x 9 = 72 so 72 ÷ 8 = 9 that means that 75 ÷ 8 is about 9 or a bit more than 9.
How could you estimate 492 ÷ 9? 9 x ___ is close to 492? 9 x 50 = 450 so 450 ÷ 9 = 50 so that
means that 492 ÷ 9 is about 50 or a bit more than 50 (an underestimate).
We can use the same strategy to estimate division of decimal numbers.
Estimate 7.5 ÷ 8: 7.5 = 75 tenths so think 75 ÷ 8 as above and so 75 tenths ÷ 8 is about 9 tenths or
0.9
You could also think 8.0 ÷ 8 = 1 so 7.5 ÷ 8 is a bit less than 1.
Estimate 4.92 ÷ 9: 4.92 = 492 hundredths so think 492 ÷ 9 as above so 0.492 ÷ 9 is about 50
hundredths or 0.5 (1/2)
You could also think 492 ÷ 10 or 490 ÷ 10 is 49 so 490 hundredths ÷ 10 is about 49 hundredths or
0.49
Instruction/Guided Practice:
Model several ways of thinking for each of the following: Estimate each quotient.
1) Tell if your estimate is an overestimate or an underestimate.
a) 21.73 ÷ 4 b) 29.311 ÷ 3 c) 97.113 ÷ 2
2) The decimal point is missing in each product or quotient. Estimate to place the decimal point.
Show your thinking.
a) 14.0604 ÷ 3 = 46868
b) 10.521 ÷ 8 = 1315125
c) 379.081 ÷ 4 = 9475
Estimate to find which would be the better deal. Which is a closer estimate? How do you know?
- A large pizza for $23.99 shared between 6 people OR a medium pizza for $14.99 shared
between 4 people
Practice
The decimal point is missing in each quotient.
Use estimation to place each decimal point.
a) 8.2 ÷ 2 = 41 b) 3.81 ÷ 3 = 127 c) 1.992 ÷ 8 = 249 d) 9.45 ÷ 5 = 189 e) 11.916 ÷ 9 = 1324
f) 62.8 ÷ 8 = 785
How can we find exact quotients?
Find the quotient of 392 ÷ 4. Have students find the quotient in their notebooks. Share strategies.
How could you multiply to check?
How can this help us find the quotient of 39.2 ÷ 4 or 3.92 ÷ 4?
How could we find 26.32 ÷ 8? Model this on the board.
Practice. Find each quotient. Estimate to place the decimal point.
a) 15.27 ÷ 3 b) 2.304 ÷ 4 c) 5.76 ÷ 8 d) 8.088 ÷ 6 e) 2.316 ÷ 2
Eric cycled 2.25 km in 5 min. Josie cycled 2.72 km in 8 min. Who travelled farther in 1 min? Show
your work.
Closure:
Wrap up - Have students work in pairs to estimate each of the following and tell which of their
estimates is closer and how they know:
- 3 videos games at $24.30/game OR 5 teen magazines at $8.89/magazine
- 9 glasses of fruit smoothies at $2.59/glass OR 4 veggie pitas at $4.69/pita
Differentiation:
Use of multiple intelligences as students will recognize units of measurement:
1) Logical/Mathematical (students analyze, test, solve)
3) Verbal-Linguistic (students articulate, discuss)
4) Interpersonal (students confer, coordinate, interact)