Lesson 10

The purpose of this warm-up is for students to interpret and connect base-ten diagrams and equations and describe how they work. This will be useful when students choose their own representations and methods for subtraction during center activities. Although students may notice and wonder many things about these representations, connections to how the representations show subtracting tens from tens and ones from ones are the important discussion points. As they compare the representations, students develop their skill with place value and operation language  (MP6).

• Groups of 2
• Display the image.
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”
• 1 minute: quiet think time

• “Discutan con su pareja cómo pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Share and record responses.

• “Ambas representaciones muestran maneras de encontrar el valor de ​​​​\(66 - 28\). ¿En qué se parecen? ¿En qué son diferentes?” // “Both of these representations show ways to find the value of \(66 - 28\). How are they the same? How are they different?” (Both show taking tens from tens and ones from ones. Both show decomposing a ten. One uses base-ten diagrams and one uses only numbers and equations.)

The purpose of this activity is for students to learn stage 5 of the Target Numbers center. Students subtract two-digit numbers to get as close to 0 as possible. For the introduction of this stage, invite students to count by 10 to 100 and represent their count with base-ten blocks. Then, they take turns rolling the 3 cubes to get a number to subtract. They choose one of the numbers on the cubes to represent the tens and a different number to represent the ones. Students subtract their tens and ones from the starting number. The difference becomes the first number in the next equation. The player who gets closest to 0 in 6 rounds, without going below 0, is the winner.

• Each group of 3 students will need 3 number cubes.

• Each group of 2 students will need base-ten blocks to represent at least 20 tens and 18 ones.

• Groups of 2
• Give each student a copy of the recording sheet. 
• Give each group 3 number cubes and access to base-ten blocks.
• “Vamos a aprender una nueva forma de jugar ‘Números objetivo’. Cada uno va a empezar con 100 y van a competir para ver quién llegar primero a un número menor que 10” // “We are going to learn a new way to play Target Numbers. You and your partner will start with 100 and race to see who can reach a number less than 10 first.”
• “En vez de usar tarjetas para decidir si quitar decenas o unidades, van a usar dados numéricos para hacer un número de dos dígitos y después restar ese número” // “Instead of using cards to decide whether to take away tens or ones, you will use number cubes to create a two-digit number and then subtract that number.”
• “Primero, cada uno represente 100 con bloques en base diez” // “First, represent 100 with base-ten blocks."
• As needed, invite students to count by 10 to 100 using the base-ten blocks or invite student to share how they might represent 100 with the blocks.
• “Cuando sea su turno, lancen los 3 dados. Escojan un número que represente las decenas y un número que represente las unidades. Después, muestren la resta usando bloques y escriban una ecuación en su hoja de registro” // "When it’s your turn, roll all 3 number cubes. Pick 1 number to represent the tens and one number to represent the ones. Then show the subtraction with your blocks and write an equation on your recording sheet.”
• “Tomen turnos para lanzar y restar hasta que alguien obtenga un número menor que 10” // “Take turns rolling and subtracting until the first person reaches a number less than 10.”
• As needed, demonstrate a round with a student volunteer. 

• 10–15 minutes: partner work

• Display equation: \(73 - \underline{\hspace{1 cm}} = \underline{\hspace{1 cm}}\)
• Draw or display number cubes showing 4, 2, and 5.
• “¿Qué números de dos dígitos pueden hacer con estos números para que al restar sea necesario descomponer una decena? ¿Cómo lo saben?” // “What two-digit numbers could you create with this roll that would make you need to decompose a ten to subtract? How do you know?” (Sample response: 24 because if you subtract by place, there are only 3 ones, so you would need to decompose to take away 4 ones.)
• “¿Qué números de dos dígitos pueden hacer para que no sea necesario descomponer una decena? ¿Cómo lo saben?” // “What two-digit numbers could you create that wouldn’t require decomposing a ten? How do you know?” (Sample response: 52 because if you subtract by place there are 3 ones and you can take away 2 ones from 3 ones.)
• “¿Qué número harían para tratar de quedar debajo de 10 lo más rápido posible? Expliquen” // “What number would you create to try to get below 10 the fastest? Explain. (54 because it’s the number that lets you take away the most tens and ones.)

The purpose of this activity is for students to choose an activity to work on that focuses on addition and subtraction within 100 or building fluency with addition and subtraction within 20. Students choose from any stage of previously introduced centers. Stage 4 of Capture Squares is also included as an extension. 

• Target Numbers
• Capture Squares
• Five in a Row

Gather materials from:

• Target Numbers, Stages 4 and 5

• Capture Squares, Stage 3 and 4

• Five in a Row, Stage 6

• “Ahora van a escoger centros de los que ya conocemos. Una de las opciones es seguir trabajando en ‘Números objetivo: Resta números de dos dígitos’” // “Now you will choose from centers we have already learned. One of the choices is to continue Target Numbers, Subtract Two-digit Numbers.”
• Display the center choices in the student book.
• “Piensen qué les gustaría hacer primero” // “Think about what you would like to do first.”
• 30 seconds: quiet think time

• Invite students to work at the center of their choice. 
• 8 minutes: center work time
• “Escojan qué quieren hacer ahora” // “Choose what you would like to do next.”
• 8 minutes: center work time

• “¿Qué actividad escogieron? ¿Qué les gustó de la actividad que escogieron?” // “Which activity did you choose? What did you like about the activity you chose?”