Week 1 of 10

Number Detectives

Students become detectives who read the clues inside a number - how big it is, which digits it holds, and how it can be broken apart - to compare, estimate, and identify mystery numbers.

Estimated time: 45-60 minutes
Grade range: Grades 2-5
Skill focus: Number sense, Comparing numbers, Estimating, Decomposing numbers
Theme: The Number Detective Agency: cracking cases with number clues

The story

The Number Detective Agency just got a case. Someone left a single clue on the door: 'I am a three-digit number. My hundreds digit is 4, my tens digit is bigger than 7, and my ones digit is 0.' The chief hands you a magnifying glass and asks, 'Which numbers could fit?' To close the case, you'll need to read numbers the way a detective reads clues.

What you'll learn

Compare two numbers using greater than (>), less than (<), and equal to (=) by looking at place value from the largest digit first.
Estimate about how many objects are in a group by rounding to the nearest ten or hundred, and explain why an exact count is not always needed.
Decompose a number into hundreds, tens, and ones (for example, 256 = 200 + 50 + 6) and rebuild it.

Key ideas

A digit's value depends on its place in the number.
To compare numbers, line them up and check the biggest place first.
Estimating gives a fast, close-enough answer when an exact count is slow.

Words to know

Digit: One of the symbols 0-9 that make up a number.
Place value: How much a digit is worth based on its position (ones, tens, hundreds).
Greater than (>): A symbol showing the number on the left is larger.
Less than (<): A symbol showing the number on the left is smaller.
Estimate: A smart, close-enough guess made by rounding to a friendly number.
Decompose: To break a number into the parts that make it, like 256 = 200 + 50 + 6.

The lesson

Every number is made of digits, and where a digit sits tells you how much it is worth. In 256, the 2 is not just 'two' - it sits in the hundreds place, so it means 200. The 5 is in the tens place, so it means 50, and the 6 in the ones place means 6. Reading a number's places is the detective's first move.

To compare two numbers, line them up by their places and check the biggest place first. Comparing 348 and 384, both have 3 hundreds, so it's a tie there. Move to the tens: 348 has 4 tens, 384 has 8 tens. Eight tens beats four tens, so 384 is greater. We write 348 < 384. The symbol always opens toward the bigger number, like a mouth eating the larger snack.

Sometimes you don't need the exact count - you need a good guess fast. Estimating means rounding to a nearby, friendly number. If a jar looks like it has about 60 marbles, you don't have to count all 58; 'about 60' is close enough to compare jars or plan a game.

Decomposing means breaking a number into its parts. 256 comes apart into 200 + 50 + 6. Detectives do this to see a number's hidden structure, and it makes adding and subtracting much easier later in the course.

Worked examples

Compare 348 and 384 using >, <, or =.

348 < 384

Hundreds are equal (3 = 3). Move to the tens: 4 tens vs 8 tens. Since 8 tens is more, 384 is the larger number, so 348 is less than 384.

Decompose 407 into hundreds, tens, and ones.

407 = 400 + 0 + 7

The 4 is in the hundreds place (400), there are no tens (0), and the 7 is in the ones place. The 0 is a placeholder that keeps the 4 and 7 in the right spots.

About how many is 58 rounded to the nearest ten?

About 60

58 sits between 50 and 60. Because the ones digit is 8 (which is 5 or more), we round up to 60. 'About 60' is close enough for a quick estimate.

Try it: interactive practice

This is the week's practice game. Work through it right here - try each step yourself, then check your thinking.

Activity

Mystery Number Hunt

Placing a number on a line forces you to think about its size compared to its neighbors - the same reasoning you use to compare and estimate.

Case #1· find the mystery number

I am greater than 40.
I am less than 70.
I have a 5 in the tens place.
I am an even number.
I have a 0 in the ones place.

Hands-on challenge

Number Clue Cards

What you need

Index cards
Pencil
A jar of small objects to estimate (optional)

Steps

1
Write five different three-digit numbers, each on its own index card.
2
On a second set of cards, write one clue for each number (for example, 'I have 2 hundreds and my ones digit is 9').
3
Trade clue cards with a partner and try to match each clue to the right number.

You've got it when: You can explain out loud why a clue matches its number by naming the value in each place (hundreds, tens, ones).

Checkpoint

Quick checks before you move on. Try each one first, then reveal the answer.

1
Which is greater, 512 or 521? How do you know?
Show answer
521 is greater. The hundreds are equal (5 = 5), but 521 has 2 tens versus 512's 1 ten, so 521 wins at the tens place.
2
Decompose 630 into its parts.
Show answer
630 = 600 + 30 + 0.
3
Round 43 to the nearest ten.
Show answer
40, because the ones digit (3) is less than 5, so we round down.

Think about it

When would estimating be more helpful than counting the exact amount? Describe a real moment when 'about how many' is good enough.

Challenge problem

I am a three-digit number between 300 and 400. My tens digit is double my ones digit, and my ones digit is 3. What number am I?

Show hint

Start with the ones digit (3), then figure out the tens digit by doubling it. The hundreds digit must keep you between 300 and 400.

Show answer

363. The hundreds digit is 3 (to stay between 300 and 400), the ones digit is 3, and the tens digit is double 3, which is 6.

Extension · go further

Make a 'wanted poster' for a mystery number with exactly four clues so that only one number in the world fits all four. Test it on a family member.

Finished the lesson, activity, and challenge? Mark this week complete to track your progress through the 10-week course.