options: Use place value understanding and properties of operations to perform multi-digit arithmetic. (A range of algorithms may be used.)

Use place value understanding and properties of operations to perform multi-digit arithmetic.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.

Extend the counting sequence.

Use place value understanding and properties of operations to add and subtract.

Understand the place value system.

Generalize place value understanding for multi-digit whole numbers.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.

Work with numbers 11–19 to gain foundations for place value.

Understand place value.

Perform operations with multi-digit whole numbers and with decimals to hundredths.
problem_activity: Narrative
The purpose of this activity is for students to have an opportunity to apply their place value understanding to estimate quantities of objects and accurately count familiar objects.
Required Materials
Materials to Gather
Bags
Collections of objects
Required Preparation
Each group of 2 needs a bag of a collection of small objects.
Launch
Groups of 2
Display for all to see approximately 15–25 beans or other small objects.
“How many objects do you think are in this pile?”
1 minute: partner discussion
Share responses.
“How could we find out exactly?” (Count them.)
Activity
“How many objects are in 2 handfuls? Let's do an experiment.”
Give each group a bag of objects.
“Take turns and grab a handful. Estimate how many objects you both grabbed altogether. Then find out how many you have exactly.”
“You will do this experiment three times.”
5 minutes: partner work time
Monitor for students who:
count by ones
group the objects into groups of 10 and then count the tens and ones
Student Facing
Experiment 1: How many objects are in 2 handfuls?
Record an estimate that is:
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "row"}, "_value": "too low"}, {"_attributes": {"scope": "col"}, "_value": "about right"}, {"_attributes": {"scope": "col"}, "_value": "too high"}]}]}], "tbody": [{"tr": [{"td": [{"span": [{"_attributes": {"class": ["math"]}, "_value": "\\(\\phantom{\\hspace{2.5cm} \\\\ \\hspace{2.5cm}}\\)"}]}, {"span": [{"_attributes": {"class": ["math"]}, "_value": "\\(\\phantom{\\hspace{2.5cm} \\\\ \\hspace{2.5cm}}\\)"}]}, {"span": [{"_attributes": {"class": ["math"]}, "_value": "\\(\\phantom{\\hspace{2.5cm} \\\\ \\hspace{2.5cm}}\\)"}]}]}]}]}]}
Now find the exact number. ____________
Experiment 2: How many objects are in 2 handfuls?
Record an estimate that is:
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "row"}, "_value": "too low"}, {"_attributes": {"scope": "col"}, "_value": "about right"}, {"_attributes": {"scope": "col"}, "_value": "too high"}]}]}], "tbody": [{"tr": [{"td": [{"span": [{"_attributes": {"class": ["math"]}, "_value": "\\(\\phantom{\\hspace{2.5cm} \\\\ \\hspace{2.5cm}}\\)"}]}, {"span": [{"_attributes": {"class": ["math"]}, "_value": "\\(\\phantom{\\hspace{2.5cm} \\\\ \\hspace{2.5cm}}\\)"}]}, {"span": [{"_attributes": {"class": ["math"]}, "_value": "\\(\\phantom{\\hspace{2.5cm} \\\\ \\hspace{2.5cm}}\\)"}]}]}]}]}]}
Now find the exact number. ____________
Experiment 3: How many objects are in 2 handfuls?
Record an estimate that is:
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "row"}, "_value": "too low"}, {"_attributes": {"scope": "col"}, "_value": "about right"}, {"_attributes": {"scope": "col"}, "_value": "too high"}]}]}], "tbody": [{"tr": [{"td": [{"span": [{"_attributes": {"class": ["math"]}, "_value": "\\(\\phantom{\\hspace{2.5cm} \\\\ \\hspace{2.5cm}}\\)"}]}, {"span": [{"_attributes": {"class": ["math"]}, "_value": "\\(\\phantom{\\hspace{2.5cm} \\\\ \\hspace{2.5cm}}\\)"}]}, {"span": [{"_attributes": {"class": ["math"]}, "_value": "\\(\\phantom{\\hspace{2.5cm} \\\\ \\hspace{2.5cm}}\\)"}]}]}]}]}]}
Now find the exact number. ____________
Student Response
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Activity Synthesis
Invite previously identified students to share.
“Did your estimates get better with practice?”
“How did organizing your objects help you to count?”
“Imagine I have 72 objects. How many would you have if you have 10 fewer than I do? What if you had 10 more?”
“If you had 72 objects, how could they be arranged in piles of 10 and ones? Are there any other ways?" (7 tens and 2 ones, 6 tens and 12 ones)


correct_option_index: 2

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