Practice A: Numbers to One Million
Chapter 1 · Consolidation 1
Mixed consolidation. Attempt problems independently before revealing the solutions.
Multiply 2,217 by 100.
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Scaling each place value by 100 gives 221,700.
How many complete groups of 100 can be made from 719,643 objects, and how many remain?
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719,643 = 7196 × 100 + 43.
Maya says a pattern 809,467, 809,517, 809,617 grows by the same amount every time. Is she right?
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The differences are 50 and 100, so the step is not constant.
Insert <, >, or =: 606,937 ___ 590,389.
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Compare the leftmost place where the digits differ: 606,937 is greater than 590,389.
Round 16,350 to the nearest 100.
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The bounding multiples are 16,300 and 16,400. The midpoint is 16,350, so the nearer benchmark is 16,400.
Round 494,742 to the nearest 1,000.
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The bounding multiples are 494,000 and 495,000. The midpoint is 494,500, so the nearer benchmark is 495,000.
Find 18,243 + 1,000. Explain which place-value units change.
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Adding 1,000 increases the number by that place-value unit, with exchanges if needed: 19,243.
How many complete groups of 100 can be made from 17,943 objects, and how many remain?
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17,943 = 179 × 100 + 43.
From 677,658 add 8 groups of 10,000.
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8 groups of 10,000 are 80,000; then add to the starting value.
Extend this pattern: 463,255, 464,255, 465,255, ___.
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Each term increases by 1,000; add that step once more.
Insert <, >, or =: 568,920 ___ 568,355.
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Compare the leftmost place where the digits differ: 568,920 is greater than 568,355.
Round 70,609 to the nearest 100.
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The bounding multiples are 70,600 and 70,700. The midpoint is 70,650, so the nearer benchmark is 70,600.
Round 282,065 to the nearest 1,000.
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The bounding multiples are 282,000 and 283,000. The midpoint is 282,500, so the nearer benchmark is 282,000.
A teacher partitions 585,500 counters into equal groups of 100. How many counters are in each group?
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Each group has 585,500 ÷ 100 = 5,855 counters.
From 17,888 add 5 groups of 100.
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5 groups of 100 are 500; then add to the starting value.
In 846,126, what is the value of the digit in the hundred-thousands place?
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The digit 8 represents 8 groups of 100,000, or 800,000.
Extend this pattern: 668,819, 673,819, 678,819, ___.
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Each term increases by 5,000; add that step once more.
Insert <, >, or =: 468,675 ___ 469,642.
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Compare the leftmost place where the digits differ: 468,675 is less than 469,642.