Number Sense
Travis Whittington
twhittington@clbs.k12.mn.us
Executive Summary
This Number Sense unit will take about fifteen class days. The unit is
composed of three parts: Part one will build students background on place
value. Part two will build students understanding of fractions with a focus on
representing them three ways. In part three students compare and find
equivalency between decimals and fractions. The overall goal of the unit is for
students to develop a greater understanding of fractions and decimals while
meeting Minnesota state standards along the way.
Minnesota Standards Covered
Standards utilized in the unit are highlighted.
Divide multi-digit numbers, using efficient and generalizable
procedures, based on knowledge of place value, including standard
algorithms. Recognize that quotients can be represented in a variety
of ways, including a whole number with a remainder, a fraction or
5.1.1.1 mixed number, or a decimal.
For example: Dividing 153 by 7 can be used to convert the improper fraction 153 to
7
the mixed number 21 76 .
Consider the context in which a problem is situated to select the
most useful form of the quotient for the solution and use the context
to interpret the quotient appropriately.
5
Number &
Operation
Divide multi-digit
numbers; solve realworld and
5.1.1.2
For example: If 77 amusement ride tickets are to be distributed equally among 4
mathematical
children, each child will receive 19 tickets, and there will be one left over. If $77 is to
problems using
be distributed equally among 4 children, each will receive $19.25, with nothing left
arithmetic.
over.
5.1.1.3
Estimate solutions to arithmetic problems in order to assess the
reasonableness of results.
Solve real-world and mathematical problems requiring addition,
subtraction, multiplication and division of multi-digit whole numbers.
Use various strategies, including the inverse relationships between
5.1.1.4 operations, the use of technology, and the context of the problem to
assess the reasonableness of results.
For example: The calculation 117 ÷ 9 = 13 can be checked by multiplying 9 and 13.
5
Number &
Operation
Read and write decimals using place value to describe decimals in
Read, write,
terms of groups from millionths to millions.
represent and
compare fractions
For example: Possible names for the number 0.0037 are:
and decimals;
5.1.2.1
37 ten thousandths
recognize and write
equivalent fractions;
3 thousandths + 7 ten thousandths;
convert between
a possible name for the number 1.5 is 15 tenths.
fractions and
decimals; use
Find 0.1 more than a number and 0.1 less than a number. Find 0.01
fractions and
5.1.2.2 more than a number and 0.01 less than a number. Find 0.001 more
decimals in realthan a number and 0.001 less than a number.
world and
mathematical
situations.
Order fractions and decimals, including mixed numbers and
improper fractions, and locate on a number line.
5.1.2.3 For example: Which is larger 1.25 or
6
5
?
Another example: In order to work properly, a part must fit through a 0.24 inch wide
space. If a part is
1
4
inch wide, will it fit?
Recognize and generate equivalent decimals, fractions, mixed
numbers and improper fractions in various contexts.
5.1.2.4
For example: When comparing 1.5 and 19
, note that 1.5 = 1 1 = 1 6 = 18 , so 1.5
12
2
12
12
< 19 .
12
Round numbers to the nearest 0.1, 0.01 and 0.001.
5.1.2.5 For example: Fifth grade students used a calculator to find the mean of the monthly
allowance in their class. The calculator display shows 25.80645161. Round this
number to the nearest cent.
5.1.3.1
Add and subtract decimals and fractions, using efficient and
generalizable procedures, including standard algorithms.
Model addition and subtraction of fractions and decimals using a
variety of representations.
5.1.3.2
Add and subtract
fractions, mixed
numbers and
decimals to solve
real-world and
mathematical
problems.
For example: Represent
2
1
+
3
4
and
2
1
3
4
by drawing a rectangle divided into 4
columns and 3 rows and shading the appropriate parts or by using fraction circles or
bars.
5.1.3.3
Estimate sums and differences of decimals and fractions to assess
the reasonableness of results.
For example: Recognize that 12 25 - 3 34 is between 8 and 9 (since
2
5
< 34 ).
Solve real-world and mathematical problems requiring addition and
subtraction of decimals, fractions and mixed numbers, including
5.1.3.4 those involving measurement, geometry and data.
For example: Calculate the perimeter of the soccer field when the length is 109.7
meters and the width is 73.1 meters.
Pretest
By the end of this unit, students should be able to answer the following questions correctly. MCA III
sampler questions relating to the unit are included.
1. Which number has a 5 in the ten-thousandths place?
A. 0.20815
B. 0.30256
C. 0.40571
D. 0.50098
2. Draw an area model to show the fraction
2/5
3. Johan’s race time was 45.03 seconds. Kyle’s race time was 0.1 second
less than Johan’s time. What was Kyle’s race time?
A. 44.03 seconds
B. 44.93 seconds
C. 45.13 seconds
D. 45.14 seconds
4. What is 0.45831 rounded to the nearest thousandth?
A. 0.45
B. 0.458
C. 0.459
D. 0.4583
5. Use the set model to show the fraction.
5/6
6. Compare, fill in the box.
3/5 [ ] 5/6
A. <
B. >
C. =
7. Compare, fill in the box.
A. <
B. >
C. =
2/4 [ ] 4/8
8. Compare, fill in the box.
.73 [ ] 3 / 4
A. <
B. >
C. =
9.
10.
11.
Table of Contents/Pacing Guide
Part 1
Day 1 – Pre-test.
Day 2 – Millionaire
Day 3 – Dare to Compare Millionaire
Day 4 – Rational Number Project #9
Day 5 – Decimal Drama
Day 6 – Rounding Races
Part 2
Day 7 – Fractions: Area model
Day 8 – Fractions: Set model
Day 9 – Fractions: Length model
Day 10 – Fractions: The big three
Day 11 – Equivalent Fractions
Part 3
Day 12– Mixed and Improper Fractions
Day 13 –Fractions to Decimals
Day 14 – Fractions Compared to Decimals
Day 15 – Review Day
Day 16 – Post-test.
Note: All materials are ordered and attached as referenced in the plan.
Day 1
(Pre-test)
Standards Covered:
5.1.1.3 - Estimate solutions to arithmetic problems in order to assess the reasonableness of results.
5.1.2.1 - Read and write decimals using place value to describe decimals in terms of groups from millionths to
millions.
5.1.2.5 - Round numbers to the nearest 0.1, 0.01 and 0.001.
5.1.2.2 - Find 0.1 more than a number and 0.1 less than a number. Find 0.01 more than a number and 0.01 less than
a number. Find 0.001 more than a number and 0.001 less than a number.
5.1.2.3 - Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line.
5.1.2.4 - Recognize and generate equivalent decimals, fractions, mixed numbers and improper fractions in various
contexts.
Materials: MCA Pre-test, Wrap It Up activity.
Launch: Question of the day activity, (students are given five minutes to gather their notebooks, pencils,
and answer the following question on the smart board daily before class starts, at the end, we discuss and
talk about a few answers/solutions.) “What is a number?” Discuss results and student answers.
“Today we’re going to be taking a pre-test to see how much you all know about our next unit. Remember
this helps us measure where we are starting at and where we are ending up, so be honest with yourself
and try your hardest.”
Explore: Hand out MCA Pre-Test. Once students complete the pretest they can work on the Wrap It Up
activity.
Share: Save five minutes at the end for students to share their wrap it up surveys with a neighbor.
Summarize: Use information turned in from Wrap It Up survey to pinpoint on areas that need work.
Day 2
(Millionaire)
Standards Covered:
5.1.1.3 - Estimate solutions to arithmetic problems in order to assess the reasonableness of results.
5.1.2.1 - Read and write decimals using place value to describe decimals in terms of groups from millionths to
millions.
Materials: Smartboard, paper, playing cards.
Launch: Question of the day activity, “My I pod has a battery length 86,400 seconds per charge. How would I write
that number with words?” Discuss results and student answers.
“Who wants to be a multimillionaire? Great then I have a game for you.”
Rules: In pairs (to develop social / speaking-listening skills) Students draw 7 joined boxes in a horizontal line. I have
a standard pack of playing cards with the face cards removed. I’ll shuffle them, turn over the top card and call out the
number. Students must choose a box to write this number in. The teacher also does this in secret. The cards are
turned and called until all 7 boxes are filled.
Students and teacher then display / say their number. Students who get a higher number than the teacher get 5
points. Equal to the teacher gets 3 points. Lower than the teacher 1 point. The teacher gets 10 points if he / she
beats all the students!
Note - a ten playing card is called as a zero.
Explore: After each round, student pairs will write out the number they created on their place value cards using a
chart created as a group on the Smartboard after the first round. This way there may be some confusion/teachable
moment when students aren’t quite sure on how to read their number aloud. IF this is too easy, no points for
incorrect number sentences.
Share: Students must share/play the game against someone at home; bring in a game card for homework.
Summarize: “In the game, what was the importance of place value? Did any groups have a strategy? Do you think
place value is important?”
Day 3
(Dare to Compare Millionaire)
Standards Covered:
5.1.1.3 - Estimate solutions to arithmetic problems in order to assess the reasonableness of results.
5.1.2.1 - Read and write decimals using place value to describe decimals in terms of groups from millionths to
millions.
5.1.2.5 - Round numbers to the nearest 0.1, 0.01 and 0.001.
5.1.2.2 - Find 0.1 more than a number and 0.1 less than a number. Find 0.01 more than a number and 0.01 less than
a number. Find 0.001 more than a number and 0.001 less than a number.
Materials: Smartboard, paper, spinner, and brass fastener.
Launch: Question of the day activity, “How did your homework go last night? What strategies did your opponent
use? Who won?” Discuss results and student answers.
“How did we know yesterday who got points when we revealed our numbers? Comparing numbers helps us see
which one is greater, or which one is less. So I’m switching our game up a little today, do any of you dare to
compare?”
Have students create this format (two boxes, decimal, two boxes, space, two boxes, decimal, two boxes).
[][].[][]
[][].[][]
They will also need the attached spinner cut out and assembled.
Explore: Students will play this game in pairs and rotate when they complete a match. Before the game starts
players get to choose their opponents symbol for the middle, (greater than or less than). Depending on the group,
model a game before. Once a match is complete, students must write the number sentence WITH greater than or
less than in the sentence.
Share: Students need to take this game home and share/play with someone at home. Bring in one gamecard as
homework.
Summarize: Did your strategy change from yesterday? How did the added rule of greater than or less than change
how you decided where to place your numbers?
Day 4
(Rational Number Project #9)
Standards Covered:
5.1.1.3 - Estimate solutions to arithmetic problems in order to assess the reasonableness of results.
5.1.2.1 - Read and write decimals using place value to describe decimals in terms of groups from millionths to
millions.
5.1.2.2 - Find 0.1 more than a number and 0.1 less than a number. Find 0.01 more than a number and 0.01 less than
a number. Find 0.001 more than a number and 0.001 less than a number.
Materials: Smartboard, paper, Rational Number Project Lesson #9, Lesson #9 worksheets, coloring supplies.
Launch: Question of the day activity, “How could you show how much a decimal is?” Discuss results and student
answers.
Work through the Rational Number Project Lesson #9
Explore: Students work on their own to finish pages C and D
Share: Come together as a whole group and look at different students decimal/grid solutions. Talk about where the
different place values are shown on the grid.
Summarize: “Why would this tool be useful?” “What were we trying to find out?”
Teaching Actions
Comments
Small Group/Partner Work
7. Students work in their groups to complete Student
Pages C and D. Students should use orange and
yellow crayons, pencils or markers to show the
amounts shaded.
Wrap Up
8. Refer students to the first problem on Student Page
C. Show this on the large classroom grid using
orange strips and yellow squares. Ask: What part of
the grid is covered? What are the different ways we
can describe that amount:
·
·
and
.
You want students to see the number
and
3-tenths and 4 hundredths more
If you showed the amount using 34 yellow
squares, how can you describe this amount?
· 34 out of 100
·
·
You want students to understand .34
as the sum of two parts:
as a single entity as well:
.34 =
.
+
.34 = 34 out of 100 or
34-hundredths
9. Explain: You can also record that amount covered in
this way: 0.34
10. Ask: How can you make sense of this way of naming
that amount by comparing 0.34 to this way of
writing the amount?
+
. (Connect this to
showing 3 orange strips and 4 yellow squares).
11. Ask: How can you make sense of this way of naming
that amount by comparing .34 to 34 out of 100 or
? (Connect this to showing the amount as 34
yellow squares).
12. Possible explanations:
·
3 is in the tenths place so it is
; 4 is in the
100ths place so it is
·
Lesson 9
If you consider how many 100ths are covered
then it’s 34-hundredths.
©RNP 2009
3
Teaching Actions
Comments
4. Return to the grid and draw lines from left to right.
· Ask: How has the whole changed?
· How many small squares in all? If I color 3
small squares yellow, what fraction of the
whole square is yellow? What fraction is not
yellow?
· How many small squares in 1-tenth of the
square? What can you say about 10hundredths and 1-tenth?
Consider how the grids and the colors
support these students’
understanding of decimal size.
5. Direct students to use their orange and yellow
crayons, pencils or markers to show the amounts
found in the table below on the 10 x 10 grids on
Student Page B.
T: Which is bigger .75 or.9? What do
you picture when you see the 75hundredths?
S: I picture 7 oranges and 5 yellow
squares.
T: And the tenths?
S: I see 9 oranges.
T: So then which is bigger?
S: 9-tenths.
T: Picture .28 on the 10 x 10 grid. If
you added 6-hundredths more. Is
the amount shaded more or less
6. Encourage a variety of ways to describe the amounts
than the grid?
on the board. You want students o be flexible in how
they interpret the decimal amount. Record what
S S: It would be less than
students say on the board.
Show this amount
3 out of 10 equal parts
Describe what you see
3-tenths;
; 3 orange
strips
34 out of 100 equal parts
;
and
; 34-
hundredths; 34 yellow
squares; 3 orange strips and
4 yellow squares more
2 out of 10 equal parts and 6
out of 100 equal parts
and
;
; 26-
hundredths; 2 orange strips
and 6 yellow squares; 26
yellow squares
55 hundredths
; 55 yellow squares; 5
orange strips and 5 yellow
squares;
8 tenths
and
; 8 orange strips; 80
yellow squares;
2
©RNP 2009
. Because
you add up the hundredths you line
them up. I did it with the fraction
grid in my head. If you have 2
oranges and 8 yellows and you add
6 more yellows that would change
that 10 to an orange and you have 4
left.
As you can see from the previous
examples, students’ order and
estimation skills with decimals are
improved when they have strong
mental images for decimals related to
this grid model. Consider one more
example of student’s thinking based
on the 10 x 10 grid:
2.3 - .05. I imagine this one with a
grid so 2 full grids and then
there’s 3 tenths so you minus 5 of
the hundredths because 3 tenths
is the same as 30 hundredths.
Cross out 5 hundredths which
leaves you with 25. Two and 25hundredths.
Lesson 9
Teaching Actions
Comments
13. Repeat for the other examples on Student Page C
and D. Students should record the different ways
discussed directly on their papers:
· Name the amount on the grid
· Describe verbally
· Record as fractions in two ways
· Write as a decimal
· Make connections between the two ways of
writing the amount as fractions and the
decimal symbol.
14. End the lesson by asking students: When do you use
decimals in your everyday life?
· Money
· Metric measurement
· Baseball statistics
· Track statistics
Translations:
·
·
·
·
4
Concrete to verbal
Concrete to verbal to symbols
Concrete to verbal to pictures to symbols
Symbols to pictures to symbols
©RNP 2009
Lesson 9
Name______________________
Lesson 9/Student Page A
Name
Lesson 9 / Student Page B
Lesson 9/Warm Up
Order the fractions from smallest to
largest. Be ready to explain your
reasoning.
Day 5
(Decimal Drama)
Standards Covered:
5.1.1.3 - Estimate solutions to arithmetic problems in order to assess the reasonableness of results.
5.1.2.1 - Read and write decimals using place value to describe decimals in terms of groups from millionths to
millions.
5.1.2.2 - Find 0.1 more than a number and 0.1 less than a number. Find 0.01 more than a number and 0.01 less than
a number. Find 0.001 more than a number and 0.001 less than a number.
5.1.2.3 - Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line.
Materials: Smartboard, paper, spinners.
Launch: Question of the day activity, “Whittington’s Waterpark uses chlorine tablets to kill bacteria in the pool. State
standards say that there needs to be a chlorine level of 2.7651339 mL per liter of water. My pools are at 2.7651347
mL of chlorine per liter of water. Who has more chlorine in their pool? “Discuss results and student answers.
Explore: “Using our place value chart we created on the Smartboard, We’re going to add in a decimal place and
start working through defining the various decimal place values. See if you and a partner can come up with names
for seven places behind the decimal. Then as a group we’ll fill in our chart.
“Get out your spinners from yesterday and create three different decimal numbers out to the seventh decimal place,
challenge yourself and write a number sentence for your three numbers. Write your three number sentences on the
board when finished.
Once everyone has their three sentences up, try to order them from least to greatest. Ask if this is different from
ordering whole numbers and why. If students struggle, write it in standard form: example, two tenths = .2
Share: “Where do we use decimals outside the classroom?” Generate a list on the Smartboard.
Summarize: “How is ordering decimals different from ordering whole numbers? Why? Where do you see decimals
outside of the math classroom?”
Day 6
(Rounding Races)
Standards Covered:
5.1.1.3 - Estimate solutions to arithmetic problems in order to assess the reasonableness of results.
5.1.2.1 - Read and write decimals using place value to describe decimals in terms of groups from millionths to
millions.
5.1.2.5 - Round numbers to the nearest 0.1, 0.01 and 0.001.
5.1.2.2 - Find 0.1 more than a number and 0.1 less than a number. Find 0.01 more than a number and 0.01 less than
a number. Find 0.001 more than a number and 0.001 less than a number.
Materials: Smartboard, paper, spinner
Launch: Question of the day activity, “What does it mean to round numbers? Do you think we could round decimals?
Give me an example of where you think this does or doesn’t work.” Discuss results and student answers.
Have students create this format.
[][][].[][][]
Similar to the games played on previous days (See day 1), choose a student to play against to model the game play
for the class (great time to cover decimal rounding). Before starting pairs play paper rock scissors, one match,
winner = player one. Player one decides whether we’re playing for the greatest value or the least value, player two
decides to what place value they will round.
Once rules are set, players use their spinners to fill their boxes, then they round according to the rules they have
picked. Student that has either the greatest or least number (depending on the rules they picked wins that round)
Explore: Let students play the game, rotating after each match.
Share: Ask students to share their strategies with other pairs, “How do you get the greatest value?” “How do you get
the least value?” “Has the game now changed since previous days?”
Summarize: Did rounding affect anyone’s match? Is rounding different on the left side of the decimal compared to
the right side?
Day 7
(Fractions: Area Model)
Standards Covered:
5.1.2.3 - Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line.
5.1.2.4 - Recognize and generate equivalent decimals, fractions, mixed numbers and improper fractions in various
contexts.
Materials: Smartboard, paper, inch grid paper, Navigating through Number and Operations in Grades 3-5 Lesson:
“Fraction Models p.27”, fraction circles CD-rom, tiles,
Launch: Question of the day activity, “I cooked a large pepperoni pizza, and I cut it into 31 pieces. If I ate 13 of
those pieces, what would be the fraction of pizza I ate?” Discuss results and student answers.
Review numerator and denominator. Remind them that denominator indicates the pieces of the whole,.
Go through the engage activity from Navigating through Number and Operations in Grades 3-5 pg. 28-30.
Explore: Introduce the area model for displaying fractions, work through the lesson using the fraction circles.
Distribute manipulatives and have students start working on fraction model charts made from folding paper into
fourths (2x2 array). Let them choose four fractions to represent on the charts. Challenge them to use different
representations (circles, squares, etc.) for their area models/fraction pictures.
Share: Select a few students to show their different area models on the Smartboard.
Summarize: “What shapes or manipulatives did you use to represent fractions in your area models?” “Does the
shape you choose change the value of the fraction?” “Could I use any shape to represent a fraction?””
Day 8
(Fractions: Set Model)
Standards Covered:
5.1.2.3 - Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line.
5.1.2.4 - Recognize and generate equivalent decimals, fractions, mixed numbers and improper fractions in various
contexts.
5.1.2.3 - Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line.
Materials: Smartboard, paper, inch grid paper, Navigating through Number and Operations in Grades 3-5 Lesson:
“Fraction Models p.27”, fraction circles and fraction strips from CD-rom, Cuisenaire rods, tiles, counters, other
manipulatives that could be used to represent fractions.
Launch: Question of the day activity, create four different area models for students to answer with the corresponding
fractions. After discussing, choose one to challenge students to write using a different shape (something odd to work
with) to represent the fractions.
Explore: Using the earlier six fractions, introduce the set model from Navigating through Number and Operations in
Grades 3-5 pg. 31. Go through the six fractions on the Smartboard using manipulatives to introduce the set models
and answer questions. Repeat yesterday’s activity of students folding paper into fourths to create set models. Let
them choose four NEW fractions to create using manipulatives listed in materials.
Share: Have students compare their set models to a neighbor. Then pose the following summary questions for them
to discuss together.
Summarize: “Do you need manipulatives to do the set model?” “Could you draw something to represent fractions in
the set model that isn’t a manipulative?” “Does it change the fraction?”
Day 9
(Fractions: Length Model)
Standards Covered:
5.1.2.3 - Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line.
5.1.2.4 - Recognize and generate equivalent decimals, fractions, mixed numbers and improper fractions in various
contexts.
5.1.2.3 - Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line.
Materials: Smartboard, paper, inch grid paper, Navigating through Number and Operations in Grades 3-5 Lesson:
“Fraction Models p.27”, fraction strips from CD-rom, Cuisenaire rods, tiles, rulers.
Launch: Question of the day activity, provide rulers for students. “I had a one foot of licorice, and I wanted to divide
it up equally for six students. Could you draw a picture that shows how I could divide it up quickly? You may need to
work diagonally on your notebook paper to draw a one-foot piece of licorice. How much does each person get?
Explore: Introduce the length model from Navigating through Number and Operations in Grades 3-5 pg. 31. Use
the fraction strips to go through six created fractions on the Smartboard Use manipulatives to introduce the length
model concretely and answer questions. Repeat yesterday’s activity of students folding paper into fourths to create
length models. Let them choose four NEW fractions to create using manipulatives listed in materials.
Share: Have students compare their charts with a neighbor. Discuss similarities and differences.
Summarize: “How are all three methods alike? Which method do you understand the best?” “Where would each
model work the best?”
Day 10
(Fractions: The Big Three)
Standards Covered:
5.1.2.3 - Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line.
5.1.2.4 - Recognize and generate equivalent decimals, fractions, mixed numbers and improper fractions in various
contexts.
5.1.2.3 - Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line.
Materials: Smartboard, paper, inch grid paper, Navigating through Number and Operations in Grades 3-5 Lesson:
“Fraction Models p.27”, fraction circles and fraction strips from CD-rom, Cuisenaire rods, tiles, counters, other
manipulatives that could be used to represent fractions, rulers.
Launch: Question of the day activity, Create three addition problems using different fraction models with common
denominators to test students’ previous knowledge of adding fractions (looking ahead for the next unit). Discuss
results and student answers.
Explore: Introduce the big three (area model, set model, length model) review chart. Go over a fraction as a group
and represent it using the three models. Have students pick three fractions from a common class generated list on
the Smartboard (so there aren’t too many of the same) to revisit and complete three charts for display.
Share: Before students put up their fractions, have them order their charts from least to greatest. Then find a partner
and do the same now with six charts.
Summarize: “How were you able to tell when fractions were bigger then each other?” “Was it always easy to see the
greater fraction?” “How could we really know a fraction is bigger when the denominators don’t match?”
Day 11
(Equivalent fractions)
Standards Covered:
5.1.2.3 - Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line.
5.1.2.4 - Recognize and generate equivalent decimals, fractions, mixed numbers and improper fractions in various
contexts.
Materials: Smartboard, paper, notecards.
Launch: Question of the day activity, ”What does it mean to be equal?” Discuss results and student answers.
Discuss fractions like ½ and 2/4, which one is bigger? Introduce equivalent fractions. Go over a variety of examples
and see if students can contribute their own ideas.
Hand out six note cards per student. Make a list of equivalent fractions on the Smartboard with denominators less
then ten for students to use as a fraction bank for their notecards. Have them create equivalent fraction cards by
writing fractions on the note cards that have an equivalent pair. Therefore each student should have three pairs of
equivalent fraction cards. Repeats are okay in this game because they will still matchup.
Explore: In groups of three, students will mix up their cards and lay them out face down in three rows of six. The
game is played like memory, each student takes a turn and turns over two cards, if they are equivalent they keep the
pair and go again. If not the cards are turned over and the next person goes. Round ends when all cards are paired
with their equivalent. Person with the most matches win.
Share: If students play their cards a few times, allow them to switch cards with another group.
Summarize: “Did anyone have a moment where they weren’t quite sure if fractions were equivalent? What did you
do to decide or figure it out?”
Day 12
(Mixed and Improper Fractions)
Standards Covered:
5.1.2.3 - Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line.
5.1.2.4 - Recognize and generate equivalent decimals, fractions, mixed numbers and improper fractions in various
contexts.
5.1.2.3 - Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line.
Materials: Smartboard, paper, spinners
Launch: Question of the day activity, ”With a partner, use both your fraction circles to show these fractions. 1 1/3, 1
2/4, 1 5/6” Discuss results and student answers.
Introduce the concepts of mixed numbers and improper fractions using the examples, show how one can be
converted to the other using examples on the board.
Have students make this format on a piece of paper.
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Explore: Pair students and using their spinners, have them make two improper fractions, then convert to mixed
numbers. Then draw a picture to represent the mixed numbers they have created, they can pick from area, set or
length models. Then as a pair decide which fraction is greater. Have them repeat at least 4 times.
Share: Bring students up to the board to share a few interesting fractions they have found
Summarize: “How did this activity go? Did anyone find it difficult to draw out some of the fractions using our models
we’ve learned?” “Which model was the easiest to use?” “Did anyone come up with any fractions that were equal?”
Discuss equivalency using student examples.
Day 13
(Fractions to Decimals)
Standards Covered:
5.1.2.3 - Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line.
5.1.2.4 - Recognize and generate equivalent decimals, fractions, mixed numbers and improper fractions in various
contexts.
5.1.2.3 - Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line.
Materials: Smartboard, paper, inch grid paper, fraction circles and fraction strips from CD-rom, Cuisenaire rods, tiles,
counters, other manipulatives that could be used to represent fractions, rulers.
Launch: Question of the day activity, “My Ipod is 7/8 full of music, while ________ Ipod is 8/10 full of music. Who’s
Ipod has more music on it? Draw a picture to show your thinking!” Discuss results and student answers.
“How do we know when one fraction is bigger then the other? I saw many of you draw pictures, is there any other
way to know the size of fractions without drawing a picture?” Introduce converting fractions to decimals via long
division. Use the board example to model.
Explore: Have students practice this concept using their fractions from the previous days. Area model, set model,
length model (4 fractions for each). Have them convert each fraction to a decimal for a total of twelve problems.
Share: Have students share their results with a neighbor. As a pair challenge them to put at least 12 decimals in
order from least to greatest.
Summarize: “Why do we need to know how to convert a fraction to a decimal?” “Can we always draw a picture or
sometimes is it not the best method?”
Day 14
(Fractions Compared to Decimals)
Standards Covered:
5.1.2.3 - Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line.
5.1.2.4 - Recognize and generate equivalent decimals, fractions, mixed numbers and improper fractions in various
contexts.
5.1.2.3 - Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line.
Materials: Smartboard, paper, rulers, Navigating through Number and Operations in Grades 3-5 Lesson: Fractions
with a point p. 41.
Launch: Question of the day activity, Give a variety of common fractions and decimals on the Smartboard, have
students copy them down and create lines to connect fractions to decimals that are equivalent. Discuss results and
student answers.
Work through a few decimal and equivalent charts using problems from the Smartboard. Have students create the
parallel number lines with a ruler as a group from Fractions with a point on pg. 51
Explore: Have students find 4 equivalent fractions and decimals from their parallel number lines. Prove that they
work by using the fraction to decimal conversion strategy from the previous day.
Share: Have students share their answers and findings with someone next to them. Together try to add two more
lines to their charts. They’ll have to decide on a fraction and then find the equivalent decimal to construct he two
extra lines. Example 1/3 = .3 repeating.
Summarize: “How does your parallel number line work?” “Was it pretty accurate?” “Would it work for a fraction like
3/7?” “What method would you have to use then?”
Day 15
(Review Day)
Standards Covered:
5.1.1.3 - Estimate solutions to arithmetic problems in order to assess the reasonableness of results.
5.1.2.1 - Read and write decimals using place value to describe decimals in terms of groups from millionths to
millions.
5.1.2.5 - Round numbers to the nearest 0.1, 0.01 and 0.001.
5.1.2.2 - Find 0.1 more than a number and 0.1 less than a number. Find 0.01 more than a number and 0.01 less than
a number. Find 0.001 more than a number and 0.001 less than a number.
5.1.2.3 - Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line.
5.1.2.4 - Recognize and generate equivalent decimals, fractions, mixed numbers and improper fractions in various
contexts.
Materials: Smartboard, Wrap It Up activity.
Launch: Question of the day activity, “What have you learned over the past three weeks?”
Explore: Use problems from earlier in the lesson to review place value (Millionaire), fraction models (area,
set, and length), fraction to decimals, comparing fractions, equivalency, etc.
Extra time play match up game.
Summarize: Wrap it Up Activity
Day 16
(Post-Test)
Standards Covered:
5.1.3.4 - Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and
mixed numbers, including those involving measurement, geometry and data.
5.1.2.5 - Round numbers to the nearest 0.1, 0.01 and 0.001.
5.1.2.2 - Find 0.1 more than a number and 0.1 less than a number. Find 0.01 more than a number and 0.01 less than
a number. Find 0.001 more than a number and 0.001 less than a number.
5.1.2.3 - Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line.
Materials: MCA Post Test
Launch: “We’re going to see how much we’ve learned over the past three weeks by taking a post-test. It’s
very similar to the one you took at the beginning of the unit, but take your time and relate the activities
we’ve done to the questions.”
Explore: Hand out MCA Post Test.
Summarize: “What was an activity you enjoyed from this unit?” “What was an activity you didn’t like?”
Use this sheet to wrap up your ideas, thoughts and questions about the last assignment/test.
One thing I remembered was…
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One thing I liked was…
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One thing I wasn’t sure of was…
_____________________________________________________________________________________
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One thing I still have questions about is…
_____________________________________________________________________________________
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Lesson 9 / Student Page D
Naming Tenths and Hundredths on a 10 x 10 Grid
Shade in the amount of the grid noted in each problem.
50 – hundredths
1-tenth and 2 hundredths