Grade 5 Place Value-­‐ Conceptual Lessons Type of Knowledge & SBAC Claim C, P 1, 4 C, P 1, 3 C, P 1 RK, C, P 1 P 1 C,P 1, 3 RK, C, P 1 Lesson Title and Objective/Description Suggested Time Frame Math Practice embedded Meter Stick Building Students use a meter long strip of paper to build a measuring tool. They estimate and measure objects in the room. They use their meter stick to compare lengths and to write lengths using both fractions and decimals in standard and expanded notation. Meter Sticks and Expanded Decimals Students use the meter sticks they built in Meter Stick Building and layering decimal cards to measure and express lengths in standard decimal form and expanded decimal form. Rounding, Estimating Decimals Students use a meter stick to round and then to develop the procedure for rounding without a meter stick. Three Meter Dash Students roll a die to get digits for each place in a length represented by a decimal. They move their markers in a race across the classroom. Practice Students practice comparing and rounding decimal values. Using meter sticks to check answers and validate explanations. Base 10 Blocks and Decimal Place Value Students represent and compare decimal values using base 10 blocks. They revisit the meaning of multiplication by a whole number and multiplication by a fraction and extend it to multiplying decimals by 10 or by 1/10. Block Dragon
Students roll a die to get digits for a decimal in a game to gather the
largest pile of base 10 blocks.
1-­‐2 days 1, 4, 5 1 day 5, 6, 7, 8 1 day 2, 5, 6 1 day 1, 2 2 days 4, 6 1-­‐2 days 1, 3, 5 1 day 1 1 PVD T1
C, P 1 Equivalent Decimal Expressions Sorting and Matching Students sort cards in standard notation, expanded notation and in words to find equivalent expressions. Some cards are then used for a Memory game. Students then complete a chart moving between the various forms. C Formative Assessment 1, 3 Students (individually or in pairs) write a response to a prompt about comparing two decimals numbers. P Practice 1 Students practice reading and writing decimal expressions in various forms. C, P Patterns in Place Value 1, 3 Students use repeated multiplication by 10 and by 1/10 on a calculator to identify the relationship between the value of adjacent places in a number. Multiplication by 1/10 is shown to be equivalent to division by 10. Exponents are introduced as a way to write repeated multiplication. RK, C How Far? 1. 2 Students place number cards on a huge number line to represent numbers between 0 and 2500, with 1 represented by a 1 cm cube. Some numbers are written using exponents such as 6 x 102. RK, C In Between 1, 2 Students place number cards on a huge number line to represent numbers between 0 and 1. Some numbers are written using expanded notation or words. Benchmark decimals are discussed and used in later rounds. All Review and Summative Assessment NOTES: 4 Week Unit Addresses Standards: NBT 1, 2, 3a, 3b, 4 Types of Knowledge: Facts (F) Procedures (P) Concepts (C ) Relational Knowledge (RK) 2 days 6, 7, 8 Half day 2, 3, 6 2 day 6, 7 1 day 1, 3, 5, 7, 8 1 day 1,2 1 day 1,2 2 days SBAC Claims: 1) Concepts & Procedures 2) Problem Solving 3) Communicating & Reasoning 4) Modeling & Data Analysis 2 PVD T2
Teacher Directions
Materials
Copies of Meter Stick Building
Meter long strips of paper, about 3-4 cm wide works well. These can be cut from
butcher paper.
Index cards cut to be 10 cm long, unmarked. At least 1 per pair.
Index cards cut to be 10 cm long, with 1 cm marks. At least 1 per pair.
A carefully selected object to be measured that is between 0.6 m and 1 m. It is best
if the object has a well defined length (not fuzzy or changeable like a pillow.)
Also, it is better if the object is not precisely between tenth measurements.
Something with a measure of 0.628 or 0.784 m would work well.
Meter Sticks (at least 1 per group, preferred is 1 per pair)
Objective
Students will develop an understanding of the first three decimal place values
through the building of a meter stick and the estimation and measurement of an
object to the tenths, hundredths and finally thousandths.
Directions
Give each student a meter strip of paper, telling them each that this length is what
we will call “one” today. Hold up the object that you have chosen to measure
today and ask them how it compares to the length of 1 that they are holding.
Hopefully they will respond that the object is less than 1 long, maybe more than ½.
Ask students to use a fraction to estimate how long the object is. Give them a
moment to think in silence, then discuss their estimate with students near them.
Select students to say their fractions until you have several with different
denominators. Ask how we could find out the length of the object and see who is
closest. Lead the class to the realization that if we are each using different
denominators it will be difficult to measure and compare how close we are.
Pass out the activity pages and have them record their fraction and some ideas
from the class discussion about the difficulty of using different denominators.
Tell the class that we will all use tenths to estimate the object and to make it easier
to visualize, you are giving them cards that are one tenth long. Ask them to use the
cards to mark off all of the tenths on their long strip.
Have students complete #3-#7 of the activity page.
IMP Activity: Meter Stick Building
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PVD T3
In #7 we are looking for an expression similar to 7 ×
1
10
.
As a class, possibly with many students coming up to the object to measure for
themselves, come to an agreement about what is the nearest tenth for everyone to
write in #8.
Before beginning the second page, tell the class we want to be even more accurate.
Ask for some suggestions about how to do this. Hopefully, you can get a response
of dividing our “one” into more parts. To do this, give everyone a “tenth” card
with 10 markings. Ask them to put these marks between each of their tenths on
their strip.
Repeat the process of what was done on page 1 with tenths on page 2 with
hundredths. Again, as a class, come to an agreement about what is the nearest
hundredth for the length of the object.
Toward the bottom of page 3 is Stage 3. Here, rather than put more marks on the
strip of paper, hand each team or pair a meter stick for them to compare with their
paper strips.
As we already know how long the object is to the nearest hundredth, the question
would be to find its length to the nearest thousandth. The students will write their
guess and label the place values in #20. They will also write this decimal as a
fraction. The next questions are to point out how we read a decimal.
If there is time at the end of the class you could have students practice reading the
length indicated by a spot on a meter stick that one of their teammates points to.
IMP Activity: Meter Stick Building
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PDV T4
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IMP Activity: Meter Sticks and Expanded Decimals
4
PVD T5
Teacher Directions
Materials
Copies of Meter Sticks and Expanded Decimals (including the pen on page 4.)
Meter Strips of paper that have been marked during the Building a Meter Stick
Activity.
Decimal cards (at least 1 per group, preferred is 1 per pair)
Meter Sticks (at least 1 per group, preferred is 1 per pair)
Objective
Students will write and understand the expanded form of a decimal to the
hundredths or thousandths place through the use of a meter stick and layered
decimal cards.
Directions
The first four objects will be measured just using the meter strip of paper and will
be measured to the nearest hundredth of a meter. Use the pen on page four as a
shared first object to measure. Walk through the directions with the class that are
on page one and make sure all students can see and agree about the length of the
picture of the pen. Have a student demonstrate in front of the class how to layer
the decimal cards.
Give students time to find three more objects with lengths between 0.1 meter and 1
meter to measure. As most teams are finishing, have each team present one object,
let the class estimate its measure, then have the team say how long it was.
Have students put away their meter strips of paper and switch to using meter sticks
to measure objects 5 to 8. Repeat the process of having teams present an object,
letting the class estimate its length, and then hearing the measured length.
If there is time, you may select up to 4 objects for students to write estimates for.
These can be written on page 3. After all estimates are complete you may collect
the papers or have them trade with other teams before measuring the objects and
seeing who was closest.
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IMP Activity: Meter Sticks and Expanded Decimals
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PVD T6
Teacher Directions
Materials
Copies of Rounding and Estimating Decimals
Meter Sticks (at least 1 per team, preferred is 1 per pair)
Directions
In teams or pairs, have students read the opening scenario. Give them a chance to
think individually then discuss in their teams and write a response before having a
class discussion.
Listen to the teams discussing so that you can choose several teams to explain their
thinking. Pick teams that had different approaches. These might include finding
pairs or groups of numbers that together make about 1 meter, looking at the tenths
place, or looking for approximate wholes, halves and quarters.
Emphasize that there are times when we want exact answers and other times when
estimating an answer will do. As students explain their thinking, identify when
they are rounding numbers. Use this context to explain that estimating means to
find an answer close to the real answer and can be done in various ways.
Rounding is a specific way to find a friendlier number close to another number.
There may be several reasonable estimates to a problem, but there is only one
correct answer when you are asked to round to a certain place value.
Part 1
Have teams find the halfway point for #1-4, then select students randomly to
present how they used the meter stick to find the answer.
Repeat for #5-8
Give students a chance to discuss, write and then read each other’s answers at the
bottom of Part 1. The halfway point is important in deciding which rounded
number another number is closer to.
Part 2
Model how to use the meter stick for rounding in #1 if necessary. Then have teams
work through half the problems and select students to present. Repeat for the
second half.
IMP Activity Rounding and Estimating Decimals
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PVD T7
Teacher Directions
Materials
Copies of Three Meter Dash
3 meter race courses ( 1 per group)
Meter Sticks (at least 1 per group, preferred is 1 per pair)
Post-it notes or other movable sticker to mark progress toward the finish.
Dice ( 1 die per group, standard 1-6 dice are good but others can be used as long
as they have only single digits on each side.)
Calculators for checking the winner’s total. (Students may be able to add these
decimal numbers because each number has 3 non-zero digits.)
Directions
Before class, set up a start and finish using tape on the floor for each group. The
start and finish should be 3 m apart.
Before distributing any materials, read through the directions with the students.
Demonstrate the rule that they must write the digit from the die after rolling it and
may not move it later, even if they get a digit they would rather have in a place
that has already been used.
Have a student show how far they would move their post-it for several sample
numbers, emphasizing the measurement of tenths, hundredths and thousandths on
a meter stick.
Have students compete in groups of 3-4. Students should watch each other roll and
write digits and everyone in the group should agree on the movement length
before a post-it is moved.
When someone from a group crosses the finish line, the entire group should write
down the winner’s distances and add them to confirm that s/he did go past 3
meters.
Faster groups can redo the race if there is time.
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IMP Activity: Three Meter Dash
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PVD T8
Teacher Directions
Materials
Copies of Base 10 Blocks and Decimal Place Value
Base 10 blocks for each team.
Directions
Give students a few minutes to explore the blocks in teams. Listen to find
what kind of experience they have with them as this will influence how
much explanation will be needed.
Before handing out the paper, ask students what they notice about the
blocks. Even more important than the fact that the rod has 10 pieces and the
flat has 100 is the relationship between the blocks. It takes 10 cubes to make
a rod. Or we might say the rod is 10 times as big as a cube. This same
relationship is true from rod to flat. If this is said by a student a heard by the
class, then the start with the lesson page will go more smoothly.
Let teams work through the first page being careful to check that each team
has identified the rods as 1/10 or 0.1 and the cubes as 1/100 or 0.01. Briefly
have some students read their responses. Be sure that teams are building the
numbers to be compared in #4.
In #5, it is important that each team recognizes that the 10 groups of 0.03
together can be represented as 0.30 or more simply as 0.3 by trading in the
hundredths for tenths.
The rest of page 2, #6 to #9, are meant to lead to the discovery that when
you multiply a decimal by 10 you will use a digit in the next place to the left
to represent the product. Not every team will notice this at the same time.
Give time to allow several teams to discover this before having some present
what they found to the class.
Page three will require that students trade in their 2 flats for 20 rods in order
to make 10 equal groups. Give students time to problem solve this situation
by getting them to repeat what is being asked, “We need to divide the 2
wholes (flats) into 10 equal groups.”
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IMP Activity: Base 10 Blocks and Decimal Place Value
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PVD T9
Again, the process of discovery and pattern recognition is more important
than having students simply hear the conclusion from someone else. It is
best if most teams can reach the conclusion and write about it before anyone
says or reads their observations to the class.
This pattern of the relationship of the value of a digit to the values on the left
and right will be explored and clarified again during the later activity
“Patterns in Place Value.”
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IMP Activity: Base 10 Blocks and Decimal Place Value
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PVD T10
Teacher Directions
Materials
Copies of Block Dragon (Repeat the same on front and back to allow
playing a second round.)
Base 10 Blocks for each group
Dice ( 1 die per group, standard 1-6 dice are good but others can be used as
long as they have only single digits on each side.)
Directions
Before distributing any materials, read through the directions with the
students. Demonstrate the rule that they must write the digit from the die
after rolling it and may not move it later, even if they get a digit they would
rather have in a place that has already been used.
Have a student show what blocks they would get for their pile for several
sample numbers, emphasizing the words “tenths” for the rods and
“hundredths” for the cubes.
Have students compete in groups of 3-4. Students should watch each other
roll and write digits and everyone in the group should agree on the blocks
that each person gets for each round.
After 3 rounds the students should each count their own and verify the totals
of the others in their group. If the students do not have experience with Base
10 blocks, you will need to demonstrate the trading of 10 hundredths for 1
tenth and 10 tenths for 1 whole.
Faster groups can redo the game if there is time.
!
IMP Activity: Block Dragon
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PVD T11
Teacher Directions
Materials
Equivalent Decimal Expressions Sort and Match Cards – 32 cards per team.
(On card stock or colored paper that makes the print not visible when face down.)
Equivalent Decimal Expressions page copies.
Objective: Students will recognize and write equivalent forms of decimals including fractions, expanded decimals and words.
Directions:
Teams of 3 or 4 receive the 32 cards (shuffled to be out of order) and are given directions to sort them (but not told what criteria to use in
sorting or how many different groups to make). After teams have found some ways in which to sort the cards, the teacher invites teams
from around the room to present their sorts to the class. Some possible sorts we might expect are:
Cards with fractions
Cards without fractions
Cards with decimals
Cards with fractions
Cards with words
Cards equivalent to 0.42
Cards equivalent to 0.024
Cards equivalent to 0.6
Cards equivalent to 0.03
Use the sorting and explaining of sorts to point out the different forms of numbers on the cards. The eight card types are:
Words matching standard form
Standard decimal
Standard fraction
Fraction product
Words matching expanded form
Expanded decimal
Expanded fraction
Expanded fraction product
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IMP Activity: Equivalent Decimal Expressions
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PVD T12
End the sorting by asking students to place them into four groups in which all of the cards of a group are equivalent forms of the same
number.
From this sort ask the students to select the 16 cards that have the four pointed star.
The remaining cards are set aside and not used for the game.
These 16 cards make eight pairs. Have students match the 8 pairs and display them for the class so that there is agreement.
Have the students play Concentration (sometimes called Memory). The 16 cards are shuffled by each team and arranged face down in a 4 x
4 grid. Students take turns selecting two cards to turn over. If they are a match, that student takes those two cards out of the grid. If they
are not a match they are turned back to face down. The student who gathers the most matching pairs wins.
After playing Concentration, the cards can be collected and the Equivalent Decimal Expressions Pages 1 and 2 can be used. Teams or
individuals can be assigned different rows to complete and share with each other or present to the class.
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IMP Activity: Equivalent Decimal Expressions
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PVD T13
Name _____________________________________ Date ____________ Period ___________
Formative Assessment
Think about the numbers 0.308 and 0.324. Explain clearly using any of the ideas you
have learned so far and complete sentences which of these two numbers is larger.
Give at least two different explanations for how you can tell which is larger. Include
drawings with your explanations when it is useful.
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IMP Activity: Formative Assessment
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PVD T14
Teacher Directions
Materials
Copies of the Formative Assessment
Directions
This assessment can be used anytime after the Rounding and Estimating Decimals
lesson to find what ideas students have developed regarding decimal place values and
their ability to communicate those ideas.
As an option, students might be given 3 minutes read and think about the question,
then allowed to discuss the question (without pencils) with a partner for 3 minutes,
before writing their response.
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IMP Activity: Formative Assessment
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PVD T15
Teacher Directions
Materials
Copies of Patterns in Place Value.
Calculators
Directions
This lesson will run most effectively with a regular back and forth pattern or teams
reading, finding patterns and attempting to answer questions, followed by a class
sharing of ideas and reading their answers. During each round it will be very
useful to listen carefully to each team in order to choose who will present their
ideas and in what order.
Teams of 3 or 4 students should first attempt to fill in the first chart and answer
questions 1 to 4. In questions 2 and 3, push students to answer both the “What is
happening?” and the “Why is this happening?” You should look for teams that are
talking about the place value to explain why the 7 is moving one place to the left
each time. Each time the 7 represents 10 times more than it did before.
After hearing students’ ideas and discussing the first page, student teams should
read and attempt questions 5 and 6 on page 2. It is important to match the level of
support and modeling you give to the class with their needs. If most of the class
cannot fill in the chart, you will need to either help them to see the patterns in the
chart or allow a successful team to explain those patterns.
Page three is very similar to page one, but in reverse. Listen for students who are
noticing this. It may be difficult to describe how the value of each place value to
the right is smaller. You may need to offer the language of “one tenth as big.”
In question 12, look for someone who has tried on the calculator 52,000 x 0.1 (one
tenth) and can show that the result is the same as 52,000 ÷ 10. Again, help with
the pattern finding to complete #13 as needed. On page four, be sure to draw
attention to the summary box.
The questions on page 5 are all opportunities to have students provide reasons for
their answers and critique the reasoning of others.
!
IMP Activity: Patterns in Place Value
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PVD T16
Teacher Directions Materials Number Cards for each round and each team. A long line (about 30 meters) with 0 marked at one end CM cubes (base 10 block cubes are usually 1 cm) one cube per team 10 meter sticks or a metric tape measure. Objective Students will approximate the location of numbers written in both standard form and using powers of 10 on a large number line. Directions Prepare a long line (about 30 meters) with only 0 marked at one end. Take the class to the number and give each team 1 cm cube. Show them the line and the starting point labeled 0. Tell them the that the cube is the size of 1 on the number line. Give them the cards for Round 1 and let the teams decide where to place the number cards. (You may need to establish a time limit if students are indecisive or attempt to measure to the correct location.) After the cards are placed, use the meter sticks or tape measure to identify the closest team for each value. Each meter is 100 cube lengths. Repeat for rounds 2, 3 and 4. In between rounds you may want to have some students explain how they estimated the locations. PVD T17
Teacher Directions Materials Number Cards for each round and each team. A 10 meter line marked with 0 at one end and 1 at the other. CM cubes (base 10 block cubes are usually 1 cm) one cube per team (optional) 10 meter sticks or a metric tape measure. Objective Students will approximate the location of decimal numbers written in various ways, including standard, expanded, fractions and words. Directions Because there is both a 0 and 1 on the line there is no need to give any further assistance in estimating the locations of the decimal numbers. You may, however, choose to give each team 1 cm cubes and explain that the cubes represent one thousandth of the number line length. Take the class to the number. Show them the line, the starting point labeled 0 and the ending point labeled 1. Give them the cards for Round 1 and let the teams decide where to place the number cards. (You may need to establish a time limit if students are indecisive or attempt to measure to the correct location.) After the cards are placed, use the meter sticks or tape measure to identify the closest team for each value. Each meter is 1/10 of the entire distance, 10 cm is a hundredth and 1 cm is a thousandth. Repeat for rounds 2, 3 and 4. In between rounds you may want to have some students explain how they estimated the locations. PVD T18