Guided Lessons

# How Many Are There?

Lay the foundation for multiplication by introducing your second graders to the concepts of skip counting and repeated addition. This lesson can be used alongside Up, Up, and Array, or separately to reinforce these important skills.
This lesson can be used as a pre-lesson for theUp, Up, and ArrayLesson plan.

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This lesson can be used as a pre-lesson for theUp, Up, and ArrayLesson plan.

Students will be able to describe an array using repeated addition.

##### Language

Students will be able to describe how many items there are in an array with grade level academic vocabulary using skip counting and/or repeated addition.

(4 minutes)
• Prior to the lesson, write the following sentence frame on the board:
• I think we should ____Because ____.
• Create a strategy bank (like a word bank) on the whiteboard with phrases and visuals that represent the phrases: count by ones, skip count, use a number line, use my fingers, mental maths, use blocks, hundreds chart, etc.
• Begin the lesson by projecting a picture of a muffin pan filled with muffins (e.g 4 x 3 muffin pan). Explain that you are making an online order and need help figuring how many muffins are in the pan.
• Ask students how you can figure out how many muffins there are in the pan. Say, "I'm not sure where to start. How can I figure out how muffins there are in the pan? Can you help me figure this problem out?"
• Read through the strategies in the strategy bank, referring to the visuals to support student understanding. Next, read through the sentence frame and model choosing a strategy from the strategy bank to complete it.
• Have students do a think-pair-share, using the sentence frame to explain what strategy they think you should use to figure out how many muffins are in the pan.
• Explain to the students that many different strategies can be used to solve the problem. Today they will learn how to use Skip counting, or counting forward using numbers other than one, and Repeated addition, adding the same amount again and again, to figure out how many items there are in all!
(8 minutes)
• Model using skip counting to figure out how many muffins are in the pan. Skip count using the muffins in the rows first (e.g. 4, 8, 12). Write the skip counting sequence on the board and circle each group of four muffins with a whiteboard marker. Ask students, "How many muffins did I add to 4 muffins to get 8 muffins? How many muffins did I add to 8 muffins to get 12 muffins?" Allow students a minute to share their ideas with an elbow partner. Clarify that you were skip counting by 4, so you added 4 muffins each time. Explain to the students that we can also figure out this problem by using repeated addition. Write 4 + 4 + 4 = 12On the whiteboard above each group of four muffins. Refer to each group of 4 muffins and say, "4 muffins combined with 4 muffins combined with 4 muffins equals 12 muffins."
• Leave the skip counting example and the repeated addition problem on the board. Circle the 12 in both examples. Explain that even though you solved the problem in different ways, you ended up with the same amount each time. Ask students, "Why do you think I ended up with the same amount each time?" and allow a few students to share their ideas with the class.
• Create a word bank with the words ForwardAnd Same. Ask students to briefly explain skip counting and repeated addition to their elbow partner, using the words from the word bank and the following sentence frame:
• I use skip counting to count ____.
• I use repeated addition to add the ____Amount more than once.
(10 minutes)
• Project another photograph on the board. This time, it may be doughnuts in a box, oranges in a box, or candies on a plate. Write, "How Many Are There?" on the whiteboard above the photograph.
• Ask students to get out their maths journals. Have students complete a pre-write where they will write down their idea for solving the problem and any questions they might have. Provide the following sentence frames to support students:
• I will use skip counting because ____.
• I will use repeated addition because ____.
• I'm not sure how to ____.
• I need help with ____.
• Read through the sentence frames and provide examples to support student understanding.
• Allow students a couple minutes to jot down their ideas.
• Provide one minute of think time after students finish writing to allow them to review their sentence. Encourage students to read their sentence aloud to themselves.
• Split students into groups of six or eight. They will make an inner circle of three or four which will face an outer circle of three or four. Say, "The purpose of this activity is for you to really think hard about how you will solve the problem. If you have experience with skip counting and repeated addition, your goal is to explain your idea for solving the problem like a mathematician. If skip counting and repeated addition are new to you, I want you to explain your strategy so your partner understands what you are saying. You can't look at your maths journal for support, but try to visualize what you wrote in your mind."
• Allow the first set of partners who are facing each other to share their ideas. Next, switch and allow students to share with another partner. Observe students as they converse and jot down notes about common or important words and phrases, together with helpful sketches or diagrams.
• Ask students to go back to their seats to complete a post-write. Have students re-read what they wrote and add on to their strategy. Encourage students to use pictures, more words, phrases, and sentences, to really dig deep into their thinking. Next, allow students a few minutes to solve the problem with a partner, using their maths journal to support them.
• Encourage students to think about the similarities and differences between their strategy and their partner's, using the following sentence frame to cultivate conversation:
• My strategy was ____(the same/different) than my partner's strategy because ____.
(8 minutes)
• Put students in small groups and pass out one of the pictures from the How Many Are There? worksheet to each group. The corresponding answer key is not necessary for this activity.
• Have the students figure out how many items are in each picture, using skip counting and/or repeated addition. Provide whiteboards and whiteboard markers for each group and allow students to reference their maths journals for support.
• Rotate around the classroom as students are solving the problem. Continue to jot down notes about the strategies, language, collaboration skills, and general strengths/challenges that come up as students problem solve.
• Allow students to share their answers with the class. Ask probing questions to dig deep into students' thinking, for example:
• How was this group's strategy the same or different from the strategy you used?
• Who can restate ____’s reasoning in a different way?
• Does anyone want to add on to this group's strategy?
• Do you agree or disagree with the way this group solved the problem? Why? Why not?

Beginning

• Go over the strategies prior to the lesson.
• Provide a table with strategies/visuals written in English and student's home language (L1) if student is literate in L1.
• Have students complete a think-pair-share with the teacher.
• Allow students to sit close to the teacher during explicit instruction.
• Define the vocabulary ForwardAnd SamePrior to the lesson in English and L1.
• Allow student to share their ideas orally with a teacher or peer during guided practise (pre-write/post-write).
• Allow students to draw any picture they'd like to represent the skip counting sequence and/or repeated addition equation during the assessment.

• Have students share their ideas without referring to the sentence frame during the introduction.
• Ask students to explain concepts of skip counting and repeated addition in their own words.
• Encourage students to use complete sentences during guided practise.
• Have students share answers to probing questions during group work.
(7 minutes)
• Write the following skip counting sequence on the board: 5, 10, 15. Under the skip counting sequence, write the following repeated addition equation: 5 + 5 + 5 = 15. Challenge students to draw a picture of muffins in a muffin pan to represent the skip counting sequence and/or the repeated addition equation. Have students record their pictures, words, and phrases in their maths journals.
• Collect student journals and use them as a formative assessment to plan future lessons along with the observations you wrote down during guided practise and group work.
(3 minutes)
• Gather students together in a circle and ask them to bring their maths journals. Have students turn to the page of their picture and show the rest of their classmates in the circle. Each student should hold their journal out towards the centre of the circle. Briefly discuss similarities/differences of a few pictures using the following probing questions:
• How is ____'s (student) picture different than ____(student)?
• How is ____'s (student) picture the same as ____(student)?

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