Two teams of students are competing to build towers of interlocking
plastic bricks. Team X has built a tower that is 100 + 40 + 4 inches
high and uses thirty thousand forty plastic bricks. Team Y has built a
tower that is twelve feet four inches high and uses 20,000 + 8,000 + 50 +
6 plastic bricks. The two teams organize their numbers. Then the two
teams use symbols to compare how high their towers are and how many
bricks each team uses. If the two teams use the height of each tower to
determine the winner, which team wins? If the two teams use the total
number of bricks in each tower to determine the winner, which team wins?
Show all your mathematical thinking.

Alternative Versions of Task

More Accessible Version

Two teams of students are competing to build towers of interlocking
plastic bricks. Team X has built a tower that uses thirty thousand forty
plastic bricks. Team Y has built a tower that uses 20,000 + 8,000 + 50 +
6 plastic bricks. The two teams organize their numbers. Then the two
teams use symbols to compare many bricks each team uses. Which team wins
by using the most bricks? Use numbers and symbols to show all your
mathematical thinking.

More Challenging Version

Three teams of students are competing to build towers of interlocking
plastic bricks. Team X has built a tower that is 100 + 40 + 4 inches
high and uses thirty thousand forty plastic bricks. Team Y has built a
tower that is twelve feet four inches high and uses 20,000 + 8,000 + 50 +
6 plastic bricks. Team Z has built a tower that is 4¾ yards high and
uses twenty-nine thousand four plastic bricks. The three teams organize
their numbers. Then the three teams use symbols to compare how high
their towers are and how many bricks each team uses. If the three teams
use the height of each tower to determine the winner, which team wins?
If the three teams use the total number of bricks in each tower to
determine the winner, which team wins? Show all your mathematical
thinking.

Whole Number and Decimal Place Value Unit

The Whole Number and Decimal Place Value
Unit involves understanding and representing the relative position,
magnitude and relationships within the numeration system in order to
answer questions such as:

How can you use the additive property of place value to decompose this number?

How can you use the multiplicative property of place value to describe the meaning of each digit in the number 9,876,543.21?

How can you use the base ten property of place value to explain the
relationship between each of the digits in the number 5,555,555.55?

How can you use base ten blocks or money to represent this decimal? What is ONE?

Standards covered in this Unit include: 4.2A, 4.2B, 4.2C, 4.2D, 4.2E, 4.2F, 4.2G, 4.2H, 4.3G

Exemplars Task-Specific Evidence

This task requires students to read, write and compare multi-digit whole
numbers in a variety of forms. Students may use inequality symbols to
compare the multi-digit numbers.

TEKS Mathematical Process Standards

4.1A Apply mathematics to problems arising in everyday life, society, and the workplace.

4.1B Use a problem-solving model that incorporates analyzing given
information, formulating a plan or strategy, determining a solution,
justifying the solution, and evaluating the problem-solving process and
the reasonableness of the solution.

4.1D Communicate mathematical ideas, reasoning, and their implications using
multiple representations, including symbols, diagrams, graphs, and
language as appropriate.

4.1E The student is expected to create and use representations to organize, record, and communicate mathematical ideas.

4.1G Display, explain, and justify mathematical ideas and arguments using
precise mathematical language in written or oral communication.

Underlying Mathematical Concepts

Base-10 place value system

12 inches to 1 foot

Number sense to 30,040

Possible Problem-Solving Strategies

Model (manipulatives)

Diagram/Key

Chart

Number line

Possible Mathematical Vocabulary/Symbolic Representation

Model

Diagram/Key

Chart

Number line

Base-10 blocks

Equivalent/Equal to

Inequality

Greater than (>)/Less than (<)

Place value

Ones, tens, hundreds

Property

Expanded notation

Total/Sum

Difference

Inches, “

Feet, ‘

Height

Gross

Per

Odd/Even

Dozen

Possible Solutions

Team Y wins by having the tallest tower. Team X wins by using the most bricks in the tower.

More Accessible Version Solution

Team X wins by using the most bricks in the tower.

More Challenging Version Solution

Team Z wins by having the tallest tower. Team X wins by using the most bricks in the tower.

Possible Connections

Below are some examples of mathematical connections. Your students may discover some that are not on this list.

144 inches is a gross.

The 2 towers are a total of 292 inches.

144 inches is 12 feet or a dozen feet.

The 2 towers are a total of 58,096 bricks.

Both towers use an even number of bricks.

58,096 ÷ 2 would be 29,048 bricks per tower.

Relate to a similar task and state a math link.

Solve more than one way to verify the answer.

Both totals of bricks have a 0 in the hundreds place.

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The Exemplars program is designed to assess students' problem-solving and mathematical-communication skills. It also supports higher-level thinking and extension of mathematical reasoning.