Explore · place value
Write 803,060,004 in expanded form, including its nonzero place values.
Singapore Math 5A · Independent learning
Numbers to One Billion
Learning target: Represent, read, compare, and decompose numbers through one billion; use digit values accurately.
Begin with the exact prerequisite checkpoint below. Afterward, explain why your strategy works, not merely which procedure to use.
Opening task
Prerequisite check (before instruction)
Attempt without help. A weak prerequisite signals review of 4A or 4B material, not a failed 5A lesson.
Write the value of the 7 in 47,082.
How many hundreds make 5,000?
Lesson-specific prerequisite checkpoint
Do this without a worked example. If you cannot explain it, review the earlier skill before continuing.
In 40,306, what is the value of the 3?
Understand the idea
Represent, read, compare, and decompose numbers through one billion; use digit values accurately.
One billion is 1,000,000,000 (one followed by nine zeros). A digit has a face value (0–9) and a position. Build numbers by multiplying each nonzero digit by its place value. Zeros hold empty places so 305 million is not 35 million. Compare numbers from the greatest place left to right, and check each number on a scaled number line.
Vocabulary focus: place-value positions, inverse scaling, round-number factors. Make a small labeled model, work through the arithmetic, and explain the result in words.
Watch for: Confusing digit position with digit value or losing place-holding zeros.
Model to study: Nine-/ten-position place-value chart and scaled number line.
Worked examples
Worked examples 1 · place value
In 405,050,001, what is the value of the digit 5 in the millions place?
Solution: 5,000,000
Why: The digit 5 is in the millions place, so 5 × 1,000,000 = 5,000,000.
Worked examples 2 · compare
Which is larger, 302,070,004 or 302,770,004, and by how much?
Solution: 302,770,004; by 700,000
Why: Compare corresponding place values from left to right; subtract 302,770,004 − 302,070,004 = 700,000.
Worked examples 3 · place value
Write 502,090,001 in expanded form, including its nonzero place values.
Solution: 5 × 100,000,000 + 2 × 1,000,000 + 9 × 10,000 + 1
Why: 5 is in the hundred-millions place, 2 in millions, 9 in ten-thousands, and 1 in ones.
Check understanding
Check understanding 1 · place value
In 401,090,003, what is the value of the digit 1 in the millions place?
Check understanding 2 · compare
Which is larger, 405,020,003 or 405,120,003, and by how much?
Guided practice
Guided practice 1 · place value
Write 603,020,001 in expanded form, including its nonzero place values.
Guided practice 2 · place value
In 704,080,002, what is the value of the digit 4 in the millions place?
Guided practice 3 · compare
Which is larger, 404,090,006 or 404,290,006, and by how much?
Independent practice
Independent practice 1 · place value
Write 706,040,008 in expanded form, including its nonzero place values.
Independent practice 2 · place value
In 303,050,009, what is the value of the digit 3 in the millions place?
Independent practice 3 · compare
Which is larger, 606,020,004 or 606,120,004, and by how much?
Independent practice 4 · place value
Write 905,040,003 in expanded form, including its nonzero place values.
Independent practice 5 · place value
In 904,080,003, what is the value of the digit 4 in the millions place?
Challenge and error analysis
Challenge and error analysis 1 · worked-error diagnosis
Error-analysis notebook: Learner notebook (LESSON): “706,060,007 has zeros that do not matter, so I rewrite the number as 7,667.” Identify exactly which written step or assumption fails, correct it, and independently solve this new task: In 706,060,007, what is the value of the digit 6 in the millions place?
Challenge and error analysis 2 · reasoning transfer
Reasoning and transfer: Solve, then explain a different way to check your answer (inverse operation, estimate, model, or units as appropriate). Which is larger, 301,050,008 or 301,450,008, and by how much?
Targeted mastery: model, calculate, explain
These additional original examples address specific 5A mastery requirements. Compare the visual and the reasoning before trying the independent questions.
Targeted 1 · targeted mastery: name
Write 1,000,000,000 in words and name its highest place.
Solution: one billion; billions place
Why: A 1 in the billions place has value 1,000,000,000. The nine zeroes hold all smaller places.
Targeted 2 · targeted mastery: name
Write 405,030,006 in words. Explain the zero placeholders in all three place-value periods.
Solution: four hundred five million thirty thousand six
Why: In words: four hundred five million thirty thousand six. Separate into three-digit periods: 405 | 030 | 006. The 405 million period is four hundred five million: the 0 holds the ten-millions place. The 030 thousands period means 0 hundred-thousands, 3 ten-thousands and 0 thousands. The 006 ones period means 0 hundreds, 0 tens and 6 ones. These five zeros preserve the correct positions even though they are not spoken individually.
Targeted 3 · targeted mastery: name
Write “seven hundred two million eight thousand forty” in digits.
Targeted 4 · targeted mastery: name
Which number is one billion: 100,000,000 or 1,000,000,000? Explain.
Exit check
Exit check 1 · compare
Which is larger, 909,080,001 or 909,780,001, and by how much?
Exit check 2 · place value
Write 204,090,002 in expanded form, including its nonzero place values.
Target for independent mastery: all exit-check problems correct plus a justified explanation. A tutor may reteach the concept if calculations are correct without meaningful reasoning.