Lesson 19

The purpose of this Number Talk is to elicit strategies and understandings students have for subtracting fractions and mixed numbers, particularly cases where it is necessary to rewrite a whole number as a fraction, or decompose it into a different whole number and fraction, in order to perform subtraction. These understandings will be helpful later in this lesson when students subtract multi-digit numbers that involve decomposing units.

• Display one expression.
• “Give me a signal when you have an answer and can explain how you got it.”

• 1 minute: quiet think time
• Record answers and strategy.
• Keep expressions and work displayed.
• Repeat with each expression.

• Highlight strategies in which students decomposed the first mixed number in each expression.
• Consider asking:
  • “Who can restate _______ 's reasoning in a different way?”
  • “Did anyone have the same strategy but would explain it differently?”
  • “Did anyone approach the expression in a different way?”
  • “Does anyone want to add on to____’s strategy?”

The purpose of this activity is to use the standard algorithm to add multi-digit numbers, taking care to compose a new unit and record it accurately. They also analyze common errors and critique the given reasoning when composing a new unit (MP3).

• Groups of 2
• “Complete the first 2 problem and then talk to your partner about any patterns you notice.”

• 3 minutes: independent work time
• 2 minutes: partner discussion
• Share and record responses.
• If needed, use the expanded form to help students make connections between the way composing a larger unit is recorded when using the standard algorithm and what is happening in each place. In the bottom line of the example here, we see 10 in the ones place and 100 in the tens place. Both partial sums do not match the assigned values of their places.

  

  

• 3–4 minutes: independent work time for the last problem.

• Ask students to share the errors they identified in the last set of questions.
• “What are some common errors when adding large numbers?”

This activity revisits the idea of decomposing a unit in one place into 10 units of the place value to its right when subtracting multi-digit numbers using the standard algorithm. Students recall how this is done as they subtract numbers in which decomposition is necessary.

To support students with understanding the context, the activity launch introduces a saree (traditional wedding attire for women in India) and the idea of family heirlooms, or gifts passed down from generation to generation.

When students create a subtraction problem that does not require decomposition of a unit when using the standard algorithm, they make use of structure and their understanding of subtraction as they choose the digits for the numbers in their difference (MP7).

This activity uses MLR7 Compare and Connect. Advances: representing, conversing

• Groups of 2
• “What do you notice and wonder about these pictures?”
• Collect student ideas.
• “In this activity, Priya is researching her family history. Let’s see what she discovers.”
• “The women in the picture are dressed in a traditional Indian garment called a ‘saree’. Sarees are made of colorful fabric and often have intricate embroidery or patterned print designs.”
• “The bracelets in the picture are also from India. Sometimes jewelry like this is used as heirlooms, or gifts that are passed down from one generation to the next.”

• Groups of 2
• 5–6 minutes: independent work time
• 3 minutes: partner work time
• As students work, listen for student discourse that includes language about the place value of the digits and when to decompose a unit.

Students may not remember when to decompose a unit or how to record regrouping. Urge students to begin to subtract by place value, either by using expanded form or lining up the digits. Ask: “What issue comes up when you subtract the ones in \(1972 - 63\)?” Allow students to explain that they don't have enough ones in the ones place to subtract 3, but they can decompose a ten to get 10 ones and add it to the 2 already there. Then consider asking:

• “How will you record all of the ones you have after you decompose a ten?”
• “How will you know if you need to decompose a unit when subtracting one number from another?”

• “Let’s do a gallery walk to see what problems you created.”
• “As you walk, discuss with a partner what you notice about the value of the digits in the numbers that were chosen.”
• 3 minutes: gallery walk
• Collect 1–2 responses from student discussions during the gallery walk.
• Share 1–2 of the responses you collected.
• 1 minute: partner discussion
• “What is the same about each of the problems you created?” (In each problem each digit is greater in the first number than in the second number)
• 2 minutes: whole-group discussion