EL Support Lesson
What Are Arrays?
Students will use addition to find the total number of objects arranged in an array.
Students will describe and discuss the characteristics of an array using grade-level academic vocabulary, sentence frames, and story problems.
- Project the How Many Apples? worksheet on the board. Ask students, "What do you notice about these two pictures?" Write the following sentence stem on the whiteboard:
- I notice ____.
- Have students turn and talk, sharing their answers with a peer. Next, say, "I want to figure out how many apples are in each picture. Where should I start?" Have students do a think-pair-share with an elbow partner, sharing their ideas. Provide students with the following sentence stem:
- I can figure out how many apples there are by ____ (insert strategy).
- Allow a student to come up to the front of the class to explain the strategies that would be the most useful in figuring out the total amount of apples. Students may count the apples individually, draw circles around groups and skip count, or refer to the rows and columns in picture B to figure out the total amount of apples.
- Explain to the students that there are 15 apples in each picture. Ask students, "Did it matter how the apples were organized when trying to figure out how many apples there were in all? Was one picture easier to solve than the other? Why or why not?"
- Have a few students share their thinking with the rest of the class.
- Write the word array on the whiteboard. Explain that arrays help us count things in an organized way, and they can also be quite pleasing to look at. Organizing objects in arrays makes sense to our mathematical brains!
- Ask students to stand and choral chant, "An array helps us count things in an organized way," two to three times. Next, have them turn and talk, saying the word "array" to their partner.
- Tell the students that today they will be exploring characteristics of arrays and using arrays to figure out the total amount of various objects.
Explicit Instruction/Teacher modeling(10 minutes)
- Project the Vocabulary Cards worksheet on the board and read through the student-friendly definitions. Refer to and explain the pictures on the vocabulary cards to support student understanding.
- Split the students into four groups and pass out one of the vocabulary cards from the Vocabulary Cards worksheet to each group (array, repeated addition, column, row). Provide each group with a large piece of white paper and coloring materials.
- Explain to the students that using arrays to represent our mathematical thinking can be a great strategy to use to solve problems. Write the following story problem on the whiteboard:
- A carton has 3 rows of bottled water with 5 bottled waters in each row. How many bottled waters are there?
- Show students a photograph of a carton and bottled water to support understanding. Sketch a picture of the word carton above the word carton and a picture of bottled water above the words bottled water.
- Read the story problem aloud and briefly reflect on the following questions, asking students to turn and talk to an elbow partner:
- What is happening in the problem?
- What will the answer tell us?
- Will the answer be a big or small number?
- Give each group five minutes to create an array, using the information from the story problem. Challenge each group to label their picture, using the word from their vocabulary card. Guide the group with the repeated addition vocabulary card to create a repeated addition equation from their array, referring to the visual on the vocabulary card for support. Support students as needed and guide them in their mathematical thinking.
- Allow each group to stand up and share their poster with the rest of the classroom. Elicit conversation by writing the following question stems on the board for students to refer to:
- Do you agree/disagree with this group's illustration? Why or why not?
- Would you add/change anything in this group's illustration? Why or why not?
Guided Practice(8 minutes)
- Present a photograph of food arranged in an array to the group (apples, oranges, doughnuts, etc.)
- Explain to the students that you want them to create a story problem that is trying to find the total amount of food. Say, "If I want to find the total amount of food, should I create an addition problem or a subtraction problem? Turn and talk to your partner, sharing what you think." Allow a few students to share their ideas aloud with the class. Clarify that today they will be creating story problems using addition to find the total amount. Encourage students to refer to the story problem on the board for support.
- Put students in partnerships and ask students to take out their math journals. Explain to the students that each of them will write their own story problem that corresponds to the array. Give students sufficient time to write their own story problem.
- Have each partnership compare story problems and explain how their partner's story problem corresponds to the array. Provide the following sentence stems/frames to support student discussion:
- The array is ____ rows with ____ objects in each row.
- Your story problem makes sense because ____.
- Your story problem doesn't make sense because ____.
- I think you need to include ____ in your story problem.
- Read through the question stems and provide a few completed examples. Explain to the students that they should try to draw an array based on their partner's story problem and see if it matches the projected photograph.
- Use the Formative Assessment: Speaking and Listening worksheet to assess students' speaking and listening goals as they converse.
- Allow students a few minutes to revise their story problems based on their partner's feedback.
Group work time(10 minutes)
- Pass out the Zooming in on Arrays worksheet to each partnership.
- Read through the directions for Part 1 and Part 2 and answer any questions students have.
- Allow students sufficient time to complete their worksheets, reminding them of important speaking, listening, and discussing goals, such as: contributing an idea, offering evidence to agree/disagree with what your partner says, and asking clarifying questions. Model a few examples of each goal.
- Rotate around the room as students are completing their worksheet with their partner. Use the Formative Assessment: Speaking and Listening worksheet to continue to listen closely and evaluate student conversations.
Additional EL adaptations
- Provide students with visual examples of strategies that can be used to figure out how many apples there are (e.g. visuals of fingers, skip counting, counting groups, etc.)
- Provide students with definitions of vocabulary in English and student's home language (L1).
- Have students work 1:1 with a teacher to discuss the meaning of the words on the vocabulary cards.
- Challenge the students to find examples of an array, column, and row, from the classroom.
- Help students come up with a story problem based on the array, using photographs, manipulatives, and pictures to support student's storytelling.
- Allow students to work in a small, teacher-led group during group work, providing support as students come up with story problem examples.
- Allow students to participate in the gallery walk with sympathetic, non-EL partners.
- Encourage students to share their thinking with the rest of the class during the introduction activity.
- Ask students to explain what an array is, using their own words.
- Challenge the students to label their picture using all of the words from the vocabulary cards (row, column, array).
- Challenge the students to come up with a repeated addition equation to represent the story problem during explicit instruction.
- Encourage students to explain their thinking in their own words, not necessarily referring to the question stems for support.
- Encourage students to explain revisions they need to make in their own words/or provide support as to why revisions weren't necessary.
- Project Part 1 from the Zooming in on Arrays worksheet.
- Give each partnership a piece of tape and ask students to tape the story problems from Part 2 up around the room.
- Hold a gallery walk and ask students to rotate around the room, reading and thinking about each of the story problems that were created to connect with the pictures in Part 1 of their worksheet.
- Provide the following sentence stems to encourage deep thinking:
- This story problem makes sense because ____.
- This story problem doesn't make sense because ____.
- I think this part of the story problem needs to change because ____.
- Collect student worksheets and use them along with the Formative Assessment: Speaking and Listening to evaluate student understanding of the lesson's objectives.
Review and closing(3 minutes)
- Allow a few students to share their findings from the gallery walk using the sentence stems for support.