The purpose of this activity is for students to consider counting back by place as a method for subtracting. Students analyze different methods for finding the value of a difference. After making connections between subtracting by place and counting back by decomposing the subtrahend, students use an open number line to show their thinking. There is not an expectation for precision with the length of the jumps, as this representation is used as a tool to get students thinking about the idea of moving along the number line. The numbers are selected so that no decomposition is needed when subtracting by place value, allowing students to focus on the structure of subtracting tens from tens, and ones from ones, using base-ten blocks, base-ten diagrams, or the number line (MP7).

• Invite previously identified students to share for each expression.
• Consider sharing work from students who use base-ten diagrams and students who use number lines or equations to make connections and show reasoning about place value.
• “What is the same and what is different between _____’s representation and _____’s representation?”
• Highlight connections based on place value across representations.

The purpose of this activity is for students to analyze equations to determine the unknown values. Students use their understanding of place value and counting within 1,000 to find the value that makes each equation true. Students are given equations with unknown addends and sums that are multiples of 100, or equations with numbers that are subtracted from multiples of 100. They use any method that works for them to find the numbers that make each equation true. Monitor for ways students use what they know about sums of 10 and of 100, and counting on or counting back by place. They may also use an open number line or base-ten diagrams, as needed, to make sense of each equation or to show their thinking. If they do use base-ten diagrams, look for ways they consider composing or decomposing units. All students will make sense of this method in upcoming lessons.

• Invite previously identified students to share how they found the value of .
• Display .
• “How could this expression help us think about this problem?” (You can start at 370 and count up to 900 to find the difference.)