Task Analysis for Division of Whole Numbers
1. Understand division action language
2. Single digit division without a remainder
3. Two digit divided by one digit without remainder
4. Three-digit division by one digit without remainder
5. Two digit divided by one digit with remainder
6. Three-digit division by one digit with remainder
7. Division of any number with or without a remainder.
CAMMP 2014
College of Education
Reading and Elementary Education
Names: Rohm, R, Schoeck, A
Integrated, Thematic Problem Solving Unit: World Cup 2014
Grade Level: 4b
Arithmetic Topic (operation): Division
HIERARCHY STEP: # 1 and 2
Understand division action language
Single digit division without a remainder
THEME PROBLEM: # 1a
There are 12 soccer players with 3 players on each team. How many teams are there?
Summary Table
Action Language: 12 grouped into sets of 3. How many sets are there?
Open Number Sentence: 12 ÷ 3=_
Manipulative:Cuisenaire Rods
Quantitative Solution: 4
Referential Meaning: teams
THEME PROBLEM: # 1b
There are 8 soccer players distributed on 2 teams. How many players are on each team?
Summary Table
Action Language: 8 grouped into 2 sets with how many in each set?
Open Number Sentence: 8÷_=2
Manipulative: Counters
Quantitative Solution: 4
Referential Meaning: players
CONCRETE MANIPULATIVE: Cuisenaire Rods and counters
REPRESENTATIONAL MANIPULATIVE: N/A
TRANSITIONAL ACTIVITIES: Computer Activities
and
STUDENT PROBLEMS:
1.There are 15 soccer balls and 5 players. How many balls can each player have?
2.The teams need to practice. There are 2 soccer fields and 10 teams. How many teams should be on each field?
3. Phillip was at the World Cup, he brought 8 dollars to spend. Hot dogs were 2 dollars, how many hot dogs can he buy?
4. 9 soccer fans were sitting in the bleachers together. There were 3 fans on each bleacher. How many bleachers were there?
5. 4 teams were left to play in the semi-finals during the World Cup. There are 2 teams on each field. How many fields will they need?
6. 6 teams enter the stadium with their flags. They are in lines of 3. How many lines of teams are there?
7. 8 coaches were in a meeting and sitting on 4 sides of a table. How many were on each side?
8. There were 12 dirty jerseys left behind in the locker room to be washed. Each player left behind 2 jerseys. How many players were in the locker room?
STUDENT ANSWER KEY:
1.Quantitative Meaning: 3
Referential Meaning: balls
2.Quantitative Meaning: 5
Referential Meaning: teams
3.Quantitative Meaning: 4
Referential Meaning: hot dogs
4.Quantitative Meaning: 3
Referential Meaning: bleachers
5.Quantitative Meaning: 2
Referential Meaning: fields
6.Quantitative Meaning: 2
Referential Meaning: lines of teams
7.Quantitative Meaning:2
Referential Meaning:coaches
8.Quantitative Meaning: 6
Referential Meaning:players
HIERARCHY STEP: # 1 and 2
Understand division action language
Single digit division without a remainder
THEME PROBLEM # 2
There are 12 soccer players distributed on 4 teams. How many players are on each team?
Summary Table
Action Language: 12 grouped into 3 sets with how many in each set?
Open Number Sentence: 12÷_=4
Manipulative: Cuisenaire Rods and counters
Quantitative Solution: 3
Referential Meaning: players
CONCRETE MANIPULATIVE: Cuisenaire Rods and counters
REPRESENTATIONAL MANIPULATIVE: N/A
TRANSITIONAL ACTIVITIES: Computer Activities
and
STUDENT PROBLEMS:
1. There are 15 soccer balls available at practice. Each player has 3 balls. How many players showed up for practice?
2. Andrew bought 4 bags of popcorn during the World Cup. He spent 8 dollars total on popcorn. How much did each bag of popcorn cost?
3. There are 9 fans that came to the World Cup together and sat evenly in 3 rows of bleachers? How many can sit on each row?
4. There are 4 teams playing in the semi-finals of the World Cup. There are 2 soccer fields. How many teams will be playing on each field?
5. There are 6 flags hung on both sides of the walkway into the stadium. How many flags are hung on each side?
6. 8 coaches were in a meeting. They were sitting on 2 sides of the table. How many were on each side?
7. 6 players put all of their jerseys in a pile to be washed. There were 12 jerseys in the pile. How many jerseys did each player put in the pile?
8. 10 teams are practicing for their game. There are 5 teams on each field how many fields are in use?
STUDENT ANSWER KEY:
1.Quantitative Meaning: 3
Referential Meaning: players
2.Quantitative Meaning: 2
Referential Meaning: dollars
3.Quantitative Meaning: 3
Referential Meaning: fans
4.Quantitative Meaning: 2
Referential Meaning: teams
5.Quantitative Meaning: 3
Referential Meaning: flags
6.Quantitative Meaning: 4
Referential Meaning: coaches
7.Quantitative Meaning: 2
Referential Meaning: jerseys
8.Quantitative Meaning: 2
Referential Meaning: fields
HIERARCHY STEP: #3 Two digit divided by one digit without remainder
THEME PROBLEM: # 3
There are 32 teams participating in the World Cup. During opening ceremonies they are sitting in 4 sections. How many teams are in each section?
Summary Table
Action Language: 32 grouped into sets of 4 with how many in each set?
Open Number Sentence:32÷_=4
Manipulative:Base-10 Blocks
Quantitative Solution: 8
Referential Meaning: teams
CONCRETE MANIPULATIVE: Cuisenaire Rods
REPRESENTATIONAL MANIPULATIVE: Base-10 Blocks
TRANSITIONAL ACTIVITIES: Computer Activities
and
STUDENT PROBLEMS:
1.Lauren wanted to buy a souvenir while at the World Cup. She had 15 dollars to spend, and wanted to buy as many souvenirs as possible. Each souvenir was 5 dollars. How many can she buy?
2.12 soccer players were practicing soccer drills. The coach spilt the players into 4 groups. How many players were in each group?
3.3 players on the USA soccer team scored 9 goals. How many goals did each player score?
4.Dasha spent $21 on snacks at the World Cup. She bought snacks for 3 people. How much did she spend on each person?
5. 24 countries were at a parade for the World Cup. They were split into groups of 6. How many countries were in each group?
6.33 tickets were left to purchase for the Japan vs. Columbia match. 3 people bought all of the tickets. If each bought the same number of tickets how many tickets did they each buy?
7. 16 people traveled from Rio de Janeiro to Sao Paulo to watch soccer matches. They traveled in 2 buses. How many people were in each bus?
8. There is a section with 72 seats available at the stadium. There are 9 rows how many seats in each row?
STUDENT ANSWER KEY:
1.Quantitative Meaning: 3
Referential Meaning: souvenirs
2.Quantitative Meaning: 3
Referential Meaning: players
3.Quantitative Meaning: 3
Referential Meaning: goals
4.Quantitative Meaning: 7
Referential Meaning: dollars
5.Quantitative Meaning:4
Referential Meaning: countries
6.Quantitative Meaning: 11
Referential Meaning: tickets
7.Quantitative Meaning: 8
Referential Meaning: people
8.Quantitative Meaning: 8
Referential Meaning: seats in a row
HIERARCHY STEP: # 3 Two digit divided by one digit without remainder
THEME PROBLEM: # 4
32 teams split into sections for opening ceremonies. There are 8 teams in each section. How many sections are there?
Summary Table
Action Language: 32 grouped into sets of 8. How many times?
Open Number Sentence: 32÷8=_
Manipulative: Base-10 Blocks
Quantitative Solution: 4
Referential Meaning: sections
CONCRETE MANIPULATIVE: Counters
REPRESENTATIONAL MANIPULATIVE: Base-10 Blocks
TRANSITIONAL ACTIVITIES: Computer Activities
and
STUDENT PROBLEMS:
1. Jibraan had 15 dollars and bought 3 souvenir hats. How much did each hat cost?
2. 12 players were running drills at soccer practice. They were in groups of 3. How many different groups were running drills?
3. 9 goals were scored by team USA. Each player scored 3 goals. How many players scored goals?
4. Gregory spent 21 dollars on himself and some friends for snacks at the World Cup. Each person received 7 dollars in snacks. How many people did he buy snacks for?
5. There were 24 people on floats in a parade for the World Cup. There are 4 people on each float. How many floats are in the parade?
6. Soccer fans purchased the last 33 tickets for the USA vs. Germany match. They each purchased 11 tickets. How many fans bought tickets?
7. 16 people traveled to Sao Paulo on 8 scooters. How many people were on each one?
8. There are 72 seats available in section 34. There are 8 seats in each row. How many rows are there?
STUDENT ANSWER KEY:
1.Quantitative Meaning: 5
Referential Meaning: dollars
2.Quantitative Meaning: 4
Referential Meaning: groups
3.Quantitative Meaning: 3
Referential Meaning: players
4.Quantitative Meaning: 3
Referential Meaning: people
5.Quantitative Meaning: 6
Referential Meaning: floats
6.Quantitative Meaning: 3
Referential Meaning: fans
7.Quantitative Meaning: 2
Referential Meaning: people
8.Quantitative Meaning: 9
Referential Meaning: rows
HIERARCHY STEP: #4 Three digit division by one digit without remainder
THEME PROBLEM # 5
369 fans are watching the World Cup finals at a restaurant. They are sitting in 3 sections. How many fans are in each section?
Summary Table
Action Language: 369 grouped into sets of 3 with how many in each set?
Open Number Sentence:369÷_=3
Manipulative: Base-10 blocks
Quantitative Solution: 123
Referential Meaning: fans
CONCRETE MANIPULATIVE: N/A
REPRESENTATIONAL MANIPULATIVE: Base-10 blocks and place value chart
TRANSITIONAL ACTIVITIES: Computer Activities
and
STUDENT PROBLEMS:
1. 7 people purchased the last of the churros at the concession stand. There were 77 churros left. If everyone had the same amount of churros how many did each person purchase?
2. Morgan has been to 165 soccer games over 3 years. If she went to the same amount of games each year how many games would she have gone to each year?
3.186 people were riding in cars to a match. 3 people rode in each car. How many cars were people riding in?
4.There are drums, trombones, tubas, and clarinets in the marching band. There are 176 instruments total. If there are an even number of each instrument, how many of each instrument are there?
5. There are 7 lines to buy tickets to the World Cup. 343 people are lined up outside of the soccer stadium waiting. How many people are in each line?
6.There are 365 cars parked in the parking lot outside of the stadium. There are 5 rows of spaces and an even number of cars in each row. How many cars are in each row?
7.424 people are traveling to the World Cup on buses. There are 8 buses. How many people are on each bus?
8. 255 programs are available to give out to fans at the soccer match. There are 5 people handing them out. How many will each person hand out?
STUDENT ANSWER KEY:
1.Quantitative Meaning: 11
Referential Meaning: churros
2.Quantitative Meaning: 55
Referential Meaning: soccer games
3.Quantitative Meaning: 62
Referential Meaning: cars
4.Quantitative Meaning: 44
Referential Meaning: instruments
5.Quantitative Meaning: 49
Referential Meaning: people
6.Quantitative Meaning: 73
Referential Meaning: cars
7.Quantitative Meaning: 53
Referential Meaning: people
8.Quantitative Meaning: 51
Referential Meaning: programs
HIERARCHY STEP: # 4
Three-digit division by one digit without remainder
THEME PROBLEM # 6
369 fans are watching the world cup at a restaurant. The sections can hold 123. How many sections are there?
Summary Table
Action Language: 369 grouped into sets of 123. How many sets are there?
Open Number Sentence:369÷123=_
Manipulative: Place Value Chart
Quantitative Solution: 3
Referential Meaning: sections
CONCRETE MANIPULATIVE: N/A
REPRESENTATIONAL MANIPULATIVE: Base-10 Blocks and Place Value Chart
TRANSITIONAL ACTIVITIES: Computer Activities
STUDENT PROBLEMS:
1. 77 churros are left at the end of the game. They were packed evenly between 11 boxes. How many churros were in each box?
2. 62 cars traveled to the soccer match carrying 186 people. How many people were in each car?
3. Jackson attended 55 soccer games per year. He has been to 165 soccer games. How many years has he been going to soccer games?
4. 176 instruments were in the parade. There were 44 of each instrument. How many different types of instruments were there?
5. There are 343 people lined up to buy tickets. There are 49 people in each line. If security wants the lines to be equal how many ticket booths should they open?
6. There are 365 cars in the parking lot. They are parked in rows of 73. How many rows of cars are there?
7. 424 people riding to the World Cup on busses. Each bus can hold 53 people. How many busses are needed?
8. 255 programs have been handed out. Each usher has handed out 51. How many ushers are passing out programs?
STUDENT ANSWER KEY:
1.Quantitative Meaning: 11
Referential Meaning: churros
2.Quantitative Meaning: 3
Referential Meaning: people
3.Quantitative Meaning: 3
Referential Meaning: years
4.Quantitative Meaning: 4
Referential Meaning: different types of instruments
5.Quantitative Meaning: 7
Referential Meaning: ticket booths
6.Quantitative Meaning: 5
Referential Meaning: rows
7.Quantitative Meaning: 8
Referential Meaning: busses
8.Quantitative Meaning: 5
Referential Meaning: ushers
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