options: Geometry: students learn to classify geometric figures by their properties, and understand and compare the relationships between them. Students develop and use formulas to compute lengths, areas, and volumes, and they use transformations to generate new shapes and compare existing ones. Geometry can be studied with and without coordinates.

Measurement & Data: students learn to work with data and measure attributes such as time, money, length, area, and volume. They may learn to compare measurements to operations and convert between different units of measure.

Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.

Operations & Algebra: students learn to solve problems using algebraic thinking and operations such as addition, subtraction, multiplication, and division. They may learn to identify and explain arithmetic patterns, evaluate or manipulate numerical expressions, and reason with equations and inequalities.

Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.

Modeling: students learn to choose and use appropriate mathematics and statistics to analyze real-world empirical situations, improve decisions, and report on their conclusions and the reasoning behind them.

Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.

Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.

Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.

Statistics & Probability: students learn to analyze and produce data distributions, and build understanding of univariate and bivariate data. They learn to interpret data, make statistical inferences, justify conclusions, understand rules of probability, and use probability to make decisions.

Functions: students learn to define, use, and evaluate functions to model relationships between quantities.
problem_activity: Narrative
The purpose of this activity is for students to identify two-digit numbers or a part of a number represented in different ways, with different amounts of tens and ones. Students determine how many connecting cubes are in each bag, given clues about how many tens and ones are in the bag. Students also determine how many tens or ones are in a bag, given the total number of cubes and either the number of tens or ones. Students may use connecting cubes to make sense of the problems, and show their thinking using drawings, numbers, or words.
MLR8 Discussion Supports.
During partner work, invite students to take turns sharing their responses. Ask students to restate what they heard using precise mathematical language and their own words. Display the sentence frame: “I heard you say . . . .” Original speakers can agree or clarify for their partner.
Advances: Listening, Speaking
Required Materials
Materials to Gather
Connecting cubes in towers of 10 and singles
Launch
Groups of 4
Give students access to connecting cubes in towers of 10 and singles.
Activity
“You are going to solve problems about connecting cubes in mystery bags. You can use connecting cubes if they will help you. Show your thinking using drawings, numbers, or words.”
“You will begin by working on your own. Then you will share your thinking with a partner at your table.”
6 minutes: independent work time
“Share your thinking for problem 1 with a partner at your table.”
1 minute: partner discussion
“Share your thinking for problem 2 with a different partner at your table.”
1 minute: partner discussion
Repeat for problems 3 and 4.
Monitor for students who use connecting cubes in these ways to solve for mystery bag C:
Shows 49 as 4 tens 9 ones and moves 2 tens over to the ones cubes to have 29, shows 2 tens left.
Shows 29 ones, adds towers of 10 to get to 49.
Student Facing
Bag A has 2 ones and 5 tens.
How many cubes are in Bag A?
Show your thinking using drawings, numbers, or words.
Bag B has 4 tens and 25 ones.
How many cubes are in Bag B?
Show your thinking using drawings, numbers, or words.
Bag C has 49 cubes.
If there are 29 ones, how many tens are in the bag?
Show your thinking using drawings, numbers, or words.
Bag D has 36 cubes.
If there are only 2 tens, how many ones are in the bag?
Show your thinking using drawings, numbers, or words.
If you have time: Write a mystery bag problem about tens and ones.
Switch with your partner.
Solve.
Student Response
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Advancing Student Thinking
If students show they are adding the total number of cubes and the known tens or ones for Bag C or Bag D, consider asking:
“How could you act out this problem?”
“What do you know? What don’t you know?”
“How could you use what we’ve learned about making numbers with different amounts of tens and ones to solve the problem?”
Activity Synthesis
Invite previously identified students to share.
“How are these ways for finding the mystery number of tens the same? How are they different?” (They both used tens and ones. One person started with 29 ones and added the tens, the other person started with 4 tens 9 ones and broke apart tens until there were 29 ones.)


correct_option_index: 7