Write in word form:

Identify the digit in the tenths place:
Identify the digit in the hundredths place:

E Math Argument: True or False?

Circle your claim and write your explanation

Statement: "0.8 has the exact same value as 0.80."

TRUE FALSE

Explain why this statement is true or false using the relationship between tenths and hundredths:

Hundredths Workshop • Level 2: Core Mastery Page 2 of 2

1. Order sprinters from 1st (fastest) to 3rd:

1st: _______  •  2nd: _______  •  3rd: _______

2. Time difference between 1st & 2nd place:

Difference: hundredths (\(0.\text{___}\) s)

E The Decimal Architect: Custom Blueprint

Construct a number meeting all four criteria

• Rule 1: Value is strictly between 5.0 and 6.0.

• Rule 2: Tenths digit is an odd prime number (\(3, 5,\) or \(7\)).

• Rule 3: Hundredths digit is smaller than the tenths digit.

• Rule 4: The sum of all three digits is 14.

Your Designed Decimal:

Written in Word Form:

Expanded Form using fractions (\(\text{Ones} + \frac{\text{Tenths}}{10} + \frac{\text{Hundredths}}{100}\)):

Hundredths Workshop • Level 3: Advanced Challenge Page 2 of 2

Level 2 Solutions: Core Mastery

Curriculum Unit: Decimals

Answer Key • Page 2 of 3

Part A: Decimal Representation Matrix

Part B: Visual Models & Analysis

1. Mixed Number Model (1 whole + 35 hundredths)

• Standard Form: 1.35

• Fraction/Mixed: \(1\frac{35}{100}\) (or \(1\frac{7}{20}\))

• Word Form: one and thirty-five hundredths

2. Critical Thinking (6 single squares)

• Standard: 0.06 | Word: six hundredths

• Explanation: The model shows 6 individual tiny squares out of 100 (\(\frac{6}{100}\)). 0.6 would mean 6 entire columns of 10 squares (60 squares) are shaded.

Part C: Number Line

Point A = 0.53 (fifty-three hundredths)

Point B = 0.57 (fifty-seven hundredths)

Star at 0.51: exactly one tick mark right of 0.50.

Part D: Applications

1. Maya: 12.43 s (\(10 + 2 + 0.4 + 0.03\))

2. Saline: three and eight hundredths liters. Tenths = 0, Hundredths = 8.

Part E: True / False

Claim: TRUE

8 tenths equals 80 hundredths (\(\frac{8}{10} = \frac{80}{100}\)). Adding a trailing zero after the decimal does not change the quantity.

Hundredths Workshop • Teacher Answer Key Page 2 of 3

Teacher Resource • Solutions Guide

Level 3 Solutions: Advanced Challenge

Curriculum Unit: Decimals

Answer Key • Page 3 of 3

Part A: Case Clues & Logic Riddles

Case #1: Triple Threat

• Number is between 3 and 4 → Ones digit is 3.
• Sum of digits is 11 → Tenths + Hundredths = \(11 - 3 = 8\).
• Hundredths is 3× Tenths → \(T + 3T = 8 \implies 4T = 8 \implies T = 2\).
• Hundredths digit = \(3 \times 2 = 6\).
• Answer: 3.26

Case #2: Regrouping Vault Code

• 4 ones = 4.0
• 18 tenths = 1.8 (or 1 one and 8 tenths)
• 25 hundredths = 0.25 (or 2 tenths and 5 hundredths)
• Regroup: \(4.0 + 1.8 + 0.25 =\) 6.05
• Word form: six and five hundredths

Part B: Error Analysis (Spot the Flaw)

Claim 1: "Seven and eight hundredths = 7.8"

The Flaw: Liam placed 8 in the tenths position. 7.8 means 7 and 8 tenths (7.80). Eight hundredths requires a placeholder zero in the tenths column.

Correct Form: 7.08

Claim 2: "0.38 > 0.7 because 38 > 7"

The Flaw: Whole-number bias. Comparing place values: 0.7 has 7 tenths, while 0.38 has only 3 tenths. Alternatively, rewrite 0.7 as 0.70; 70 hundredths > 38 hundredths.

Correct Symbol: 0.38 < 0.7

Part C: Flexible Decompositions

1. \(0.84 = \mathbf{8}\text{ t} + \mathbf{4}\text{ h}\)

2. \(0.84 = 6\text{ t} + \mathbf{24}\text{ h}\)

3. \(2.15 = 1\text{ one} + \mathbf{11}\text{ t} + 5\text{ h}\)

4. Total hundredths: 127

Part D: Photo Finish Timing

• Andre: ten and nine hundredths seconds

• Carlos: ten and ninety hundredths seconds

• Ranking: 1st Andre (10.09s), 2nd Dominic (10.19s), 3rd Carlos (10.90s)

• 1st & 2nd Difference: \(10.19 - 10.09 = \mathbf{10}\) hundredths (\(0.10\) s)

Part E: The Decimal Architect

• Rule 1: Ones = 5. Rule 4: Sum = 14 → Tenths + Hundredths = 9.

• Rule 2 & 3: Tenths is odd prime (\(3, 5,\) or \(7\)) and \(H < T\).

Two Valid Solutions:

1. 5.54 (five and fifty-four hundredths; \(5 + \frac{5}{10} + \frac{4}{100}\))
2. 5.72 (five and seventy-two hundredths; \(5 + \frac{7}{10} + \frac{2}{100}\))

Hundredths Workshop • Teacher Answer Key Page 3 of 3