# Lesson 9

Solve Number Riddles

## Warm-up: True or False: Comparison Statements (10 minutes)

### Narrative

The purpose of this True or False is to elicit strategies and understandings students have for comparing two-digit numbers. These understandings will be helpful later when students will need to be able to determine numbers that are greater than or less than a given number.

### Launch

• Display one statement.
• “Give me a signal when you know whether the statement is true and can explain how you know.”
• 1 minute: quiet think time

### Activity

• Share and record answers and strategies.
• Repeat with each equation.

### Student Facing

Decide if each statement is true or false.

Be prepared to explain your reasoning.

• $$65 > 35$$

• $$65 = 75 - 10$$

• $$65 > 35 + 30$$

### Activity Synthesis

• “How can you explain your answers by describing the number of tens and ones on each side?

## Activity 1: A Number Riddle (10 minutes)

### Narrative

The purpose of this activity is for students to use their understanding of place value to find a secret number in a number riddle. Initially, students are given clues that could have more than one secret number to encourage them to think about all the possibilities. Then, they receive a clue that allows them to figure out the secret number. Students will solve this type of riddle in small groups in the next activity.

### Launch

• Groups of 3
• Give students access to connecting cubes in towers of 10 and singles.
• “We are going to solve number riddles. Let's do one together. I have chosen a secret number and will give you three clues to help you identify my number.”
• Display the clues in the student book.
• “Use the clues to identify numbers that could be my secret number. The clues aren’t in any specific order. You can use any clue to start.”

### Activity

• 4 minutes: small-group work time
• Monitor for groups of students who started with different clues.
• “Does anyone know my secret number?” (It could be 34, 44 or 54 because they all fit the clue.)
• Display and read the new clue: “My number is the sum of 24 and 20.”
• “What is my secret number?”
• Share responses.

### Student Facing

My number is less than 60.

My number has 4 ones.

My number is more than 30.

What numbers fit these clues?

Secret number: ___________

### Activity Synthesis

• “As we just saw, sometimes many different numbers fit the clues until you get the last clue. Keep that in mind as you solve Number Riddles with your group in the next activity.”

## Activity 2: More Number Riddles (25 minutes)

### Narrative

The purpose of this activity is for students to solve number riddles to find a secret number. Students work together to find the numbers that match the clues and justify why those numbers fit the clues (MP3). Then students read the last clue (shaded grey) and identify the secret number. Students rotate between riddles; it is also possible for students to remain in the same place and trade riddles.

MLR8 Discussion Supports. Prior to solving the riddles, invite students to make sense of the task and take turns sharing their understanding with their partner. Listen for and clarify any questions about the context.
Representation: Access for Perception. Provide appropriate reading accommodations and supports to ensure student access to written clues on Number Riddle Cards.
Supports accessibility for: Language, Social-Emotional Functioning

### Required Materials

Materials to Gather

Materials to Copy

• Number Riddle Cards

### Required Preparation

• Create enough riddles from the Number Riddle Cards so each group of 2 students can have a different riddle. Fold the gray cards. Place each set of clues in a bag or envelope and label based on the letter of the riddle.

### Launch

• Groups of 2
• Give each group an envelope with a riddle and access to connecting cubes in towers of 10 and singles.

### Activity

• “You are going to solve number riddles. Each riddle has four clues. One clue is shaded and folded. Keep this clue until last. Read the other clues and work together to figure out which numbers fit the clues. Once you agree on what numbers fit all the clues, read the shaded, folded clue. Work together to find the answer and write your answer in your book. Then put all the clues back in the envelope and get ready to move on to the next riddle. I will let you know when to move.”
• 20 minutes: partner work time

Secret Numbers

A: __________

B: __________

C: __________

D: __________

E: __________

F: __________

G: __________

H: __________

I: __________

J: __________

### Activity Synthesis

• Invite students to share the secret number for each riddle.

## Lesson Synthesis

### Lesson Synthesis

“Today we solved lots of number riddles. I’m really stumped on this one and need your help.“
Display the chart with only the first clue showing. “My number has more than 6 tens.“
“What could my secret number be?” (70, 75, 89, 91, any number from 70 to 120.)

Display the second clue: “My number is less than 100.”
“Now what do you know about the secret number?” (We can cross out any of the numbers that are over 100.)

Display the third clue: “My number has 8 tens.”
“How does this clue change what my secret number could be?” (Now we know we can cross off all the numbers that don’t have 8 tens.)
“What could my number be now?” (80–89)

Display the last clue: “My number is the sum of $$51 + 32$$.”
“What is my secret number? Explain your thinking.”