Standards-based assessment and Instruction

## Towers of Bricks

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.

#### 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

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

### Formal Mathematical Language and Symbolic Notation

• 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.
• Solve more than one way to verify the answer.
• Both totals of bricks have a 0 in the hundreds place.

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## Here's What People Are Saying

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.

S. Dement
Teacher

Converse, TX

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