← Find one tick interval, then read the value · Repeating Cycle Patterns

Find one tick interval, then read the value · 8 practice problems

4.NBT.A.14.NBT.A.2

Generated variants — 8

Freshly produced from the archetype’s parameters — problem, figure, and solution derived together.

Variant 1 easy answer: 1,900

Find the number marked by $\bigstar$ on the number line.

On a number line, the large tick marks are spaced evenly at $0$ , $1{,}000$ , $2{,}000$ , $3{,}000$ . Each interval between two large ticks is divided into $10$ equal small ticks. The mark $\bigstar$ points to the position $9$ small ticks past $1{,}000$ .

Show solution

1 · Understandwhat's really being asked

A number line has large ticks 1,000 apart, each split into 10 small ticks; find where the star lands.

Givens

Large ticks start at 0 and step by 1,000.
Each interval is divided into 10 equal parts.
The star is 9 small ticks past 1,000.

Unknowns

The number the star marks.

Constraints

The small ticks are equal in size.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #1 Draw a Diagram

Find the size of one small tick, then add that many from the nearest large tick.

3 · Execute3 carry out the plan

1One large interval

#8 Analyze the Units 4.NBT.A.2

Subtract two neighbouring large ticks.

1{,}000 - 0 = 1{,}000

Every big gap is the same size.

2One small tick

#1 Draw a Diagram 4.NBT.A.1

Divide the interval into its 10 equal small ticks.

1{,}000 \div 10 = 100

Splitting a place value by ten steps down one place.

3Add the small steps

#1 Draw a Diagram 4.NBT.A.2

Start at 1,000 and add 9 small ticks.

1{,}000 + 9 \times 100 = 1{,}900

Count up by the small-tick size to reach the star.

Answer: 1,900

4 · Reviewdoes it hold up?

1,900 sits between 1,000 and 2,000, as it should.

Another way: Count all small ticks from the start of the line and multiply.

Standardsmin grade 4

4.NBT.A.1 Recognize that a digit in one place represents ten times what it represents in the place to its right. — Splitting the interval into ten equal small ticks.
4.NBT.A.2 Read, write, and compare multi-digit whole numbers using place value. — Reading the multi-digit value off the line.

💡Takeaway. Find what one small tick is worth, then count up from the nearest label.

Variant 2 easy answer: 12,400

Find the number marked by $\bigstar$ on the number line.

On a number line, the large tick marks are spaced evenly at $10{,}000$ , $11{,}000$ , $12{,}000$ , $13{,}000$ . Each interval between two large ticks is divided into $10$ equal small ticks. The mark $\bigstar$ points to the position $4$ small ticks past $12{,}000$ .

Show solution

1 · Understandwhat's really being asked

A number line has large ticks 1,000 apart, each split into 10 small ticks; find where the star lands.

Givens

Large ticks start at 10,000 and step by 1,000.
Each interval is divided into 10 equal parts.
The star is 4 small ticks past 12,000.

Unknowns

The number the star marks.

Constraints

The small ticks are equal in size.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #1 Draw a Diagram

Find the size of one small tick, then add that many from the nearest large tick.

3 · Execute3 carry out the plan

1One large interval

#8 Analyze the Units 4.NBT.A.2

Subtract two neighbouring large ticks.

11{,}000 - 10{,}000 = 1{,}000

Every big gap is the same size.

2One small tick

#1 Draw a Diagram 4.NBT.A.1

Divide the interval into its 10 equal small ticks.

1{,}000 \div 10 = 100

Splitting a place value by ten steps down one place.

3Add the small steps

#1 Draw a Diagram 4.NBT.A.2

Start at 12,000 and add 4 small ticks.

12{,}000 + 4 \times 100 = 12{,}400

Count up by the small-tick size to reach the star.

Answer: 12,400

4 · Reviewdoes it hold up?

12,400 sits between 12,000 and 13,000, as it should.

Another way: Count all small ticks from the start of the line and multiply.

Standardsmin grade 4

4.NBT.A.1 Recognize that a digit in one place represents ten times what it represents in the place to its right. — Splitting the interval into ten equal small ticks.
4.NBT.A.2 Read, write, and compare multi-digit whole numbers using place value. — Reading the multi-digit value off the line.

💡Takeaway. Find what one small tick is worth, then count up from the nearest label.

Variant 3 medium answer: 250

Find the number marked by $\bigstar$ on the number line.

On a number line, the large tick marks are spaced evenly at $0$ , $100$ , $200$ , $300$ . Each interval between two large ticks is divided into $10$ equal small ticks. The mark $\bigstar$ points to the position $5$ small ticks past $200$ .

Show solution

1 · Understandwhat's really being asked

A number line has large ticks 100 apart, each split into 10 small ticks; find where the star lands.

Givens

Large ticks start at 0 and step by 100.
Each interval is divided into 10 equal parts.
The star is 5 small ticks past 200.

Unknowns

The number the star marks.

Constraints

The small ticks are equal in size.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #1 Draw a Diagram

Find the size of one small tick, then add that many from the nearest large tick.

3 · Execute3 carry out the plan

1One large interval

#8 Analyze the Units 4.NBT.A.2

Subtract two neighbouring large ticks.

100 - 0 = 100

Every big gap is the same size.

2One small tick

#1 Draw a Diagram 4.NBT.A.1

Divide the interval into its 10 equal small ticks.

100 \div 10 = 10

Splitting a place value by ten steps down one place.

3Add the small steps

#1 Draw a Diagram 4.NBT.A.2

Start at 200 and add 5 small ticks.

200 + 5 \times 10 = 250

Count up by the small-tick size to reach the star.

Answer: 250

4 · Reviewdoes it hold up?

250 sits between 200 and 300, as it should.

Another way: Count all small ticks from the start of the line and multiply.

Standardsmin grade 4

4.NBT.A.1 Recognize that a digit in one place represents ten times what it represents in the place to its right. — Splitting the interval into ten equal small ticks.
4.NBT.A.2 Read, write, and compare multi-digit whole numbers using place value. — Reading the multi-digit value off the line.

💡Takeaway. Find what one small tick is worth, then count up from the nearest label.

Variant 4 medium answer: 23,400

Find the number marked by $\bigstar$ on the number line.

On a number line, the large tick marks are spaced evenly at $20{,}000$ , $22{,}000$ , $24{,}000$ , $26{,}000$ . Each interval between two large ticks is divided into $10$ equal small ticks. The mark $\bigstar$ points to the position $7$ small ticks past $22{,}000$ .

Show solution

1 · Understandwhat's really being asked

A number line has large ticks 2,000 apart, each split into 10 small ticks; find where the star lands.

Givens

Large ticks start at 20,000 and step by 2,000.
Each interval is divided into 10 equal parts.
The star is 7 small ticks past 22,000.

Unknowns

The number the star marks.

Constraints

The small ticks are equal in size.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #1 Draw a Diagram

Find the size of one small tick, then add that many from the nearest large tick.

3 · Execute3 carry out the plan

1One large interval

#8 Analyze the Units 4.NBT.A.2

Subtract two neighbouring large ticks.

22{,}000 - 20{,}000 = 2{,}000

Every big gap is the same size.

2One small tick

#1 Draw a Diagram 4.NBT.A.1

Divide the interval into its 10 equal small ticks.

2{,}000 \div 10 = 200

Splitting a place value by ten steps down one place.

3Add the small steps

#1 Draw a Diagram 4.NBT.A.2

Start at 22,000 and add 7 small ticks.

22{,}000 + 7 \times 200 = 23{,}400

Count up by the small-tick size to reach the star.

Answer: 23,400

4 · Reviewdoes it hold up?

23,400 sits between 22,000 and 24,000, as it should.

Another way: Count all small ticks from the start of the line and multiply.

Standardsmin grade 4

4.NBT.A.1 Recognize that a digit in one place represents ten times what it represents in the place to its right. — Splitting the interval into ten equal small ticks.
4.NBT.A.2 Read, write, and compare multi-digit whole numbers using place value. — Reading the multi-digit value off the line.

💡Takeaway. Find what one small tick is worth, then count up from the nearest label.

Variant 5 medium answer: 44,000

Find the number marked by $\bigstar$ on the number line.

On a number line, the large tick marks are spaced evenly at $30{,}000$ , $35{,}000$ , $40{,}000$ , $45{,}000$ . Each interval between two large ticks is divided into $10$ equal small ticks. The mark $\bigstar$ points to the position $8$ small ticks past $40{,}000$ .

Show solution

1 · Understandwhat's really being asked

A number line has large ticks 5,000 apart, each split into 10 small ticks; find where the star lands.

Givens

Large ticks start at 30,000 and step by 5,000.
Each interval is divided into 10 equal parts.
The star is 8 small ticks past 40,000.

Unknowns

The number the star marks.

Constraints

The small ticks are equal in size.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #1 Draw a Diagram

Find the size of one small tick, then add that many from the nearest large tick.

3 · Execute3 carry out the plan

1One large interval

#8 Analyze the Units 4.NBT.A.2

Subtract two neighbouring large ticks.

35{,}000 - 30{,}000 = 5{,}000

Every big gap is the same size.

2One small tick

#1 Draw a Diagram 4.NBT.A.1

Divide the interval into its 10 equal small ticks.

5{,}000 \div 10 = 500

Splitting a place value by ten steps down one place.

3Add the small steps

#1 Draw a Diagram 4.NBT.A.2

Start at 40,000 and add 8 small ticks.

40{,}000 + 8 \times 500 = 44{,}000

Count up by the small-tick size to reach the star.

Answer: 44,000

4 · Reviewdoes it hold up?

44,000 sits between 40,000 and 45,000, as it should.

Another way: Count all small ticks from the start of the line and multiply.

Standardsmin grade 4

4.NBT.A.1 Recognize that a digit in one place represents ten times what it represents in the place to its right. — Splitting the interval into ten equal small ticks.
4.NBT.A.2 Read, write, and compare multi-digit whole numbers using place value. — Reading the multi-digit value off the line.

💡Takeaway. Find what one small tick is worth, then count up from the nearest label.

Variant 6 medium answer: 40,400

Find the number marked by $\bigstar$ on the number line.

On a number line, the large tick marks are spaced evenly at $40{,}000$ , $42{,}000$ , $44{,}000$ , $46{,}000$ . Each interval between two large ticks is divided into $10$ equal small ticks. The mark $\bigstar$ points to the position $2$ small ticks past $40{,}000$ .

Show solution

1 · Understandwhat's really being asked

A number line has large ticks 2,000 apart, each split into 10 small ticks; find where the star lands.

Givens

Large ticks start at 40,000 and step by 2,000.
Each interval is divided into 10 equal parts.
The star is 2 small ticks past 40,000.

Unknowns

The number the star marks.

Constraints

The small ticks are equal in size.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #1 Draw a Diagram

Find the size of one small tick, then add that many from the nearest large tick.

3 · Execute3 carry out the plan

1One large interval

#8 Analyze the Units 4.NBT.A.2

Subtract two neighbouring large ticks.

42{,}000 - 40{,}000 = 2{,}000

Every big gap is the same size.

2One small tick

#1 Draw a Diagram 4.NBT.A.1

Divide the interval into its 10 equal small ticks.

2{,}000 \div 10 = 200

Splitting a place value by ten steps down one place.

3Add the small steps

#1 Draw a Diagram 4.NBT.A.2

Start at 40,000 and add 2 small ticks.

40{,}000 + 2 \times 200 = 40{,}400

Count up by the small-tick size to reach the star.

Answer: 40,400

4 · Reviewdoes it hold up?

40,400 sits between 40,000 and 42,000, as it should.

Another way: Count all small ticks from the start of the line and multiply.

Standardsmin grade 4

4.NBT.A.1 Recognize that a digit in one place represents ten times what it represents in the place to its right. — Splitting the interval into ten equal small ticks.
4.NBT.A.2 Read, write, and compare multi-digit whole numbers using place value. — Reading the multi-digit value off the line.

💡Takeaway. Find what one small tick is worth, then count up from the nearest label.

Variant 7 hard answer: 113,000

Find the number marked by $\bigstar$ on the number line.

On a number line, the large tick marks are spaced evenly at $100{,}000$ , $110{,}000$ , $120{,}000$ , $130{,}000$ . Each interval between two large ticks is divided into $10$ equal small ticks. The mark $\bigstar$ points to the position $3$ small ticks past $110{,}000$ .

Show solution

1 · Understandwhat's really being asked

A number line has large ticks 10,000 apart, each split into 10 small ticks; find where the star lands.

Givens

Large ticks start at 100,000 and step by 10,000.
Each interval is divided into 10 equal parts.
The star is 3 small ticks past 110,000.

Unknowns

The number the star marks.

Constraints

The small ticks are equal in size.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #1 Draw a Diagram

Find the size of one small tick, then add that many from the nearest large tick.

3 · Execute3 carry out the plan

1One large interval

#8 Analyze the Units 4.NBT.A.2

Subtract two neighbouring large ticks.

110{,}000 - 100{,}000 = 10{,}000

Every big gap is the same size.

2One small tick

#1 Draw a Diagram 4.NBT.A.1

Divide the interval into its 10 equal small ticks.

10{,}000 \div 10 = 1{,}000

Splitting a place value by ten steps down one place.

3Add the small steps

#1 Draw a Diagram 4.NBT.A.2

Start at 110,000 and add 3 small ticks.

110{,}000 + 3 \times 1{,}000 = 113{,}000

Count up by the small-tick size to reach the star.

Answer: 113,000

4 · Reviewdoes it hold up?

113,000 sits between 110,000 and 120,000, as it should.

Another way: Count all small ticks from the start of the line and multiply.

Standardsmin grade 4

4.NBT.A.1 Recognize that a digit in one place represents ten times what it represents in the place to its right. — Splitting the interval into ten equal small ticks.
4.NBT.A.2 Read, write, and compare multi-digit whole numbers using place value. — Reading the multi-digit value off the line.

💡Takeaway. Find what one small tick is worth, then count up from the nearest label.

Variant 8 hard answer: 6,300

Find the number marked by $\bigstar$ on the number line.

On a number line, the large tick marks are spaced evenly at $5{,}000$ , $5{,}500$ , $6{,}000$ , $6{,}500$ . Each interval between two large ticks is divided into $10$ equal small ticks. The mark $\bigstar$ points to the position $6$ small ticks past $6{,}000$ .

Show solution

1 · Understandwhat's really being asked

A number line has large ticks 500 apart, each split into 10 small ticks; find where the star lands.

Givens

Large ticks start at 5,000 and step by 500.
Each interval is divided into 10 equal parts.
The star is 6 small ticks past 6,000.

Unknowns

The number the star marks.

Constraints

The small ticks are equal in size.

2 · Planchoose the strategy

#8 Analyze the Units · also uses: #1 Draw a Diagram

Find the size of one small tick, then add that many from the nearest large tick.

3 · Execute3 carry out the plan

1One large interval

#8 Analyze the Units 4.NBT.A.2

Subtract two neighbouring large ticks.

5{,}500 - 5{,}000 = 500

Every big gap is the same size.

2One small tick

#1 Draw a Diagram 4.NBT.A.1

Divide the interval into its 10 equal small ticks.

500 \div 10 = 50

Splitting a place value by ten steps down one place.

3Add the small steps

#1 Draw a Diagram 4.NBT.A.2

Start at 6,000 and add 6 small ticks.

6{,}000 + 6 \times 50 = 6{,}300

Count up by the small-tick size to reach the star.

Answer: 6,300

4 · Reviewdoes it hold up?

6,300 sits between 6,000 and 6,500, as it should.

Another way: Count all small ticks from the start of the line and multiply.

Standardsmin grade 4

4.NBT.A.1 Recognize that a digit in one place represents ten times what it represents in the place to its right. — Splitting the interval into ten equal small ticks.
4.NBT.A.2 Read, write, and compare multi-digit whole numbers using place value. — Reading the multi-digit value off the line.

💡Takeaway. Find what one small tick is worth, then count up from the nearest label.