The purpose of this Choral Count is to invite students to practice counting by 10 and notice patterns in the count. These understandings help students develop fluency and will be helpful later in this lesson when students need to be able to, given a rule, generate numerical patterns and explain features of the patterns that are not explicit in the rule. Keep the record of this count displayed for students to reference in the lesson activities.
Launch
“Cuenten de 10 en 10, empezando en 10” // “Count by 10, starting at 10.”
Record as students count.
Stop counting and recording at 150.
Activity
“¿Qué patrones ven?” // “What patterns do you see?”
1–2 minutes: quiet think time
Record responses.
None
Student Response
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Advancing Student Thinking
Activity Synthesis
“¿En qué se parece describir lo que observaron sobre los números en nuestro conteo a lo que han hecho con los patrones de figuras? ¿En qué es diferente?” // “How is describing what you notice about the numbers in our count the same as what you have been doing with shape patterns? How is it different?” (Same: Even though we were counting by 10, we noticed lots of other things that are also true. “Count by 10” is like a rule for creating a pattern. Different: It’s only numbers, there aren’t any shapes or diagrams. I’m not sure if there’s a rule.)
“Hoy vamos a generar y a describir patrones numéricos que siguen una regla. Los patrones numéricos son como lo que hacemos en el ‘Conteo grupal’. Para crear uno, necesitan saber en qué número empezar y qué hacer para obtener el siguiente número” // “Today we are going to generate and describe numerical patterns that follow a rule. Numerical patterns are like what we do in the Choral Count. To create one, you need to know what to start with and what to do to get the next number.”
“En un ‘Conteo grupal’, contamos de un número en un número hacia adelante. Los patrones numéricos pueden tener reglas, como ‘empezar en 0 y luego ir sumando 2’ o ‘empezar en 1 y luego ir multiplicando por 3’” // “In a Choral Count, we count on by a given number. Numerical patterns can have rules like start with 0 and keep adding 2 or start with 1 and keep multiplying by 3.”
Activity 1
Standards Alignment
Building On
3.OA.D.9
Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.
Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.
This activity prompts students to generate a numerical pattern that follows the rule “start with 9, keep adding 9.” They then notice and explain other features of the pattern that may include:
Patterns in even and odd numbers or digits
Patterns in the digits in the ones place or tens place
Ways the pattern can be represented with multiplication
Ways they can use familiar multiples of 10 to predict terms in the “add 9” pattern
Students use what they know about the place value and operations to explain the patterns they notice (MP7). For instance, students may reason that, because 9 is 1 less than 10, to find the value of is to find the value of and then subtract 1 group of 12 (or ) from the product. Encourage students to use drawings, diagrams, or equations as needed to explain their thinking.
MLR8 Discussion Supports. Use multimodal examples to compare the keep adding 9 pattern and counting by 10. Use verbal descriptions along with gestures, drawings, or concrete objects to show the connection between the multiples of 9 and 10. Advances: Listening, Representing
Representation: Access for Perception. Synthesis: Use pictures of the long rectangle base-ten blocks to help students visualize the patterns. For example, display a picture of eight long rectangle base-ten blocks. Count by 10 while pointing to each block. Then cross out one unit in each block and discuss how this shows that counting by 9 is like multiplying by 10 and subtracting. Supports accessibility for: Conceptual Processing, Visual Spatial Processing
Launch
Groups of 2
Read the opening paragraph as a class.
“¿En qué se parece la regla de Andre a contar de 10 en 10? ¿En qué es diferente?” // “How is Andre’s rule the same as our Choral Count by 10? How is it different?” (Same: We start with a number and then count by the same number. Adding a number over and over is like counting by a number. Different: They are different numbers. Counting by 10 is easier for me.)
30 seconds: partner discussion
“Escribamos el patrón de Andre y hablemos sobre qué observamos acerca de los números del patrón” // “Let’s create Andre’s pattern and talk about what we notice about the numbers in the pattern.”
Activity
“En silencio, trabajen unos minutos en los primeros problemas. Luego, compartan cómo pensaron y completen el resto de la actividad con su compañero” // “Take a few quiet minutes to work on the first few problems. Then share your thinking and complete the rest of the activity with your partner.”
5–6 minutes: independent work time
5–6 minutes: partner discussion
Monitor for students who explain:
Patterns with even and odd numbers
Patterns in the digits
Why the terms are the multiples of 9
How they can use what they know about multiplying by 10 to predict terms
La regla del patrón de Andre es “empezar en 9, ir sumando 9”.
Usa lo que observaste acerca del patrón de Andre para hacer algunas predicciones.
Completa la tabla con los 10 primeros números del patrón de Andre.
¿Qué observas acerca de los números del patrón de Andre? Haz al menos 2 observaciones para compartirlas con tu compañero.
seguir sumando 9
9
Escoge una observación que tu compañero o tú hayan hecho. Explica o muestra por qué crees que pasa eso.
¿Cuál es el número en la posición 12 del patrón de Andre?
¿Cuál es el número en la posición 15?
¿Cuál es el número en la posición 25?
Activity Synthesis
Invite 3–4 previously selected students to share and explain what they observed about Andre’s pattern.
Invite 2–3 students to share how they predicted the 25th number.
If no students mentioned that the list of numbers are multiples of 9, encourage them to make this observation.
If no students reason that adding 9 can be thought of as adding 10 and subtracting 1 each time, bring this understanding to their attention. Consider recording Andre’s pattern next to the count by 10 table from the Warm-up.
“En otras palabras, sumar 9 una vez es como , que es 9. Sumar 9 otra vez es como sumarle otro a 9, o , que es 18. Sumar 9 una tercera vez es como , que es 27, y así sucesivamente” // "In other words, adding 9 once means , which is 9. Adding 9 again means adding another to 9, or , which is 18. Adding 9 a third time means , which is 27. And so on."
“Sumar 9 ocho veces es lo mismo que sumar 10 ocho veces y restar 1 ocho veces, es decir, . Esto es , que es 72” // “Adding 9 eight times is the same as Adding 10 eight times and subtracting 1 eight times, or , which is or 72.”
As needed, “¿Cómo podemos usar esto para predecir cuál será el número en la posición 12 en el patrón de Andre? ¿Y en la posición 25?” // “How could we use this to predict the 12th number in Andre’s pattern? The 25th?”
Activity 2
Standards Alignment
Building On
Addressing
4.OA.C.5
Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.
Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
In this activity, students continue to generate and analyze a numerical pattern. This time, they generate a pattern that has an addition rule that they are less likely to apply with fluency. The intent is to encourage all students to use what they know about place value or properties of operations to identify features of the pattern that are not explicit in the rule as they both generate and analyze the given pattern (MP7). Although the use of the distributive property over subtraction is not expected or made explicit, the work in both activities in this lesson develops students’ intuition for seeing, for instance, that .
“Completamos un patrón que seguía la regla ‘empezar en 9, ir sumando 9’ y explicamos otros patrones que observamos en los números. Ahora veamos qué observamos acerca de un patrón que sigue otra regla” // “We completed a pattern that followed the rule “start with 9, keep adding 9” and explained other patterns we noticed in the numbers. Now, let’s see what we notice about a pattern that follows a different rule.”
Activity
“Completen la actividad con su compañero” // “Work with your partner to complete the activity.”
6–8 minutes: partner work time
Monitor for students who:
Identify different patterns in the numbers.
Reason about the numbers in the “counting by 99” column (multiples of 99), by reasoning about multiples of 100.
La regla del patrón de Elena es “empezar en 99, ir sumando 99”.
Completa la tabla con los 5 primeros números del patrón de Elena.
Examina de cerca la lista de números. Haz al menos 3 observaciones sobre los números del patrón.
ir sumando 99
99
Completa la tabla con los 5 números que siguen en el patrón de Elena.
Activity Synthesis
MLR3 Critique, Correct, Clarify
Display the response for students to consider:“Sumar 99 cinco veces es lo mismo que sumar 100 cinco veces. Solo necesitas restarle algo” // “Add 99 five times is the same as adding 100 five times. You just need to subtract some.”
Read the explanation aloud.
“¿Qué partes de esta respuesta no son claras, son incorrectas o están incompletas?” // “What parts of this response are unclear, incorrect, or incomplete?” (Adding 99 isn't the same as adding 100. It's not clear how much you would need to subtract. It's not clear how this would work for adding 99 a different number of times.)
1 minute: quiet think time
2 minute: partner discussion
Invite 2–3 groups share what they discussed. Record for all to see.
“Con su compañero, escriban una explicación ajustada” // “With your partner, work together to write a revised explanation.”
3–4 minutes: partner work time
Select 1–2 groups to read their revised draft aloud and record for all to see. Scribe as each group shares, then invite the whole class to contribute additional language and edits to make the final draft even more clear and more convincing.
“¿Cómo podemos usar nuestras explicaciones ajustadas para encontrar el vigésimo (20.°) múltiplo de 99?” // “How can we use our revised explanations to find the 20th multiple of 99?” (Find and subtract from it.)
Lesson Synthesis
“Hoy generamos patrones numéricos que siguen una regla. Tal como lo hicimos con los patrones de figuras, observamos otras características del patrón que no estaban en la regla” // “Today we generated numerical patterns that follow a rule. Just like we did with shape patterns we noticed other features in the pattern that weren’t in the rule.”
“Aunque la regla del patrón de Andre era simple, ‘empezar en 9, ir sumando 9’, ¿qué más observamos?” // “Even though the rule for Andre’s pattern was simple - “start with 9, keep adding 9” - what else did we notice?” (even and odd patterns, the ways the digits in the numbers changed each time, that all the numbers were multiples of 9)
“¿Cómo explicaron lo que observaron hoy en los patrones? ¿Qué hicieron otros que les ayudó a entender lo que ellos observaron?” // “How did you explain what you noticed in the patterns today? What did others do that helped you understand what they noticed?” (I used equations to show decomposing numbers to make a ten. I used equations to show how each number was a multiple of 9. It helped to have drawings and diagrams.)
Standards Alignment
Building On
Addressing
4.OA.C.5
Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.
Students may not see that the digit in the ones place decreases by 1 each time the pattern increases by 9. Consider asking:
“¿Cómo encontraste el número que sigue en el patrón de Andre? ¿Qué observaste a medida que completabas el patrón?” // “How did you find the next number in Andre’s pattern? What did you notice as you completed the pattern?”
“¿Qué patrones ves en la lista de números que se obtiene al seguir la regla de Andre?” // “What patterns do you see in the list of numbers that follow Andre’s rule?”
