I am particularly proud of a recent lesson plan I wrote with my classmate Gabby White. It’s a second grade math lesson on investigating multiplication. It’s a pretty good sample of how in-depth we’ve been diving into writing math lessons this semester. This is the first lesson I’ve written where I feel like I’ve really laid out every single step. I thought I’d share it on the blog for others to use in the classroom and to also give prospective students a picture of what lesson planning looks like at Columbia. The photos are from Thanksgiving Break and a bit from some lovely artwork I recently saw at Boone Elementary. Enjoy!
Common Core State Standards:
Determine whether a group of objects (up to 20) has an odd or even number of members, e.g. by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.
Interpret products of whole numbers, e.g. interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
1. How can you solve the same problem using repeated addition and multiplication?
2. How are multiplication sentences and addition sentences the same? How are they different?
3. How are equal sized groups connected to multiplication?
1. Repeated addition and multiplication are connected and can help me find the same answer to a problem that has equal groups.
2. I can multiply numbers by combining equal groups.
3. I can use objects, pictures, and numbers to solve multiplication problems.
Content Knowledge and Skills:
• In pairs, students will know how to write a repeated addition problem as a multiplication sentence by solving the problem “4 fives equals 20” with 100% accuracy in their journals and verbally sharing their solution and how they found it with their partner.
• Students will know that they can use multiple strategies to solve the same problem by participating in a whole class discussion on how they solved the problem of “How many fingers are there on four hands?” and by verbally sharing at least one strategy they used with another student.
• Individually, students will be able to demonstrate their understanding of equal groups and the phrase “groups of” by drawing one picture that has at least three equal groups in it (e.g. a picture of a garden with 4 rows of flowers that each contains 5 flowers) and including a descriptive sentence under their picture that uses the phrase “groups of.”
• Individually, students will be able to make connections between repeated addition and multiplication by writing four sentences in their journals about two different ways they could represent and solve the problem “4 fives equals 20.”
• In pairs, students will be able to make the connection between multiplication and equal groups by writing one repeated addition sentence in their journals and having their partner represent that sentence using manipulatives or a drawing.
• Students will solve the problem of “How many shoes are five children wearing?” Students can use objects, drawings, or notations to solve the problem. Teacher will observe how each student solves the problem and the strategies they use.
• Students will solve the problem of “How many fingers are there on 4 hands?” Students can use objects, drawings, or notations to solve the problem. Teacher will observe students and ask questions about how they found the solution.
The teacher will be looking for the students to use the methods to solve the equal group problems including:
• Using counters, cubes, or picture to represent the groups in each problem
• Whether the students physically counted the objects by ones
• Whether the students were able to skip count by 2 or 5
• Whether the students represented the problem using an addition sentence
• Whether the students represented the problem using a multiplication sentence
• Whether the students used a function table
• Whether the students wrote out the “groups of” to solve the problem
• For Students who are ELL: Teacher will ask students to point to their hands, feet, ears, and eyes as their classmates list objects that come in pairs. Teacher will also explicitly teach the vocabulary word pair as an object that comes in 2’s by using the word pair when pointing to eyes, hands, feet, and ears. Teacher will also give the student a flashcard that visually shows the meaning of the word. Teacher will pair an ELL student with a gifted student who can help them draw pictures of the items on the charts that their group generates of things that come packaged in groups. This same partner will help scaffold the words “equal groups”, “multiplication”, and “repeated addition” by pointing to the types of problems as they are written in their journals and explicitly helping the ELL student use these phrases while describing their strategy for solving the problems. Teacher will visually model the concept of the word “groups” as it connects to multiplication and repeated addition.
• For Students who are Gifted: Teacher will have gifted students solve a problem with items that are not in equal groups. The teacher will ask the student to write out whether they can solve the problem using multiplication and why or why not.
Teacher will have children brainstorm objects that come in twos (pairs) and list their suggestions on chart paper. Students may list hands, feet, ears, and eyes. Teacher will ask students to point to items that come in pairs in the classroom and say the words aloud for the students who are ELL. Teacher will ask for 5 student volunteers to stand at the front of the room. Teacher will then ask students how many shoes these students are wearing. Once the 5 children have taken their seats, the teacher will ask students to work out the problem in pairs. The teacher will tell students they may use counters, drawings, or notation. Teacher will ask students to show their work in their math journal.
Plans for Informal Assessment:
Teacher will observe how the students solve the problem and the strategies they use, and then record it next to their names on the roster.
1. Teacher will ask students to label their chart paper “Things that Come in Twos,” “Things that Come in Threes,” “Things That Come in Fours,” and “Things That Come in Fives. Teacher will ask the students to write out objects on their chart papers with their small group desk cluster. Teacher will ask for student volunteers to share some of their ideas with the whole class.
2. Next, teacher will ask the class to individually solve the problem “How many fingers are there on 4 hands?” Teacher will tell students that they can use the counters, drawings, or notation. After students have completed the problem, the teacher will have students spend one minute sharing their strategy with their partner. Next, teacher will have students share the ways in which they solved the problem with the whole class. Teacher will encourage students to ask each other questions about their solutions. The teacher will ask students “Was it necessary for you to draw fingers, or was it enough to represent the fingers with lines or dots?” Teacher will encourage the students to use the language “groups of” when discussing the finger problem. Teacher will demonstrate this by writing on the board “How much is 3 groups of 4?” Teacher will ask for a student to volunteer to write it as a multiplication sentence on the board.
3. Next, the teacher will write 5+5+5+5 = 20 on the board, and ask the students “what do each of the 5’s represent?” The teacher will ask the students “Is there another way to show the problem?” The teacher will write “4 fives equals 20” on the board. The teacher will ask the students how they can show this as a multiplication sentence in their journals. Teacher will ask them to share their answer with their neighbor. The teacher will ask the students “How are these two number sentences alike and different?” The teacher will have the students compare the addition sentence and the multiplication sentence in their journals. The teacher will structure this by giving the sentence starter, “I can show the answer to “4 fives equals 20” in two ways.” The teacher will ask the students to describe two ways they could represent and solve this problem and for the students to write at least four sentences about this. The teacher will have students share their answers with the class.
4. Teacher will have the students write a repeated addition sentence in their math journal. Teacher will ask the students to share their sentence with their partner and have their partner show the sentence by representing it with equal groups (manipulatives or drawing). Students will then write the multiplication sentence in their journal next to the addition sentence.
5. Teacher will ask students to draw a picture that has equal groups in it (a picture of a garden with 4 rows of flowers that each contains 5 flowers). Teacher will ask the students to write a sentence under their picture that describes it using the phrase, “groups of.” Teacher will have students share their pictures with a partner and have the partner write out the addition and multiplication sentences.
Plans for Informal Assessment:
Teacher will ask students to explain the different strategies they used to solve the finger problem. Teacher will then ask students in the classroom to explain what their classmate did to solve the problem in their own words.
Student Guided Practice:
1. In groups, students will list things that come in 2’s, 3’s, 4’s, and 5’s on chart paper. Students will share some of their ideas with the class.
2. Individually students will solve the problem “How many fingers are there on 4 hands?” Students can choose to use objects, drawings, or notations, to solve the problem. As a whole class, students will share their solutions and strategies. A student volunteer will write the multiplication sentence 3×4 on the board.
3. Students will write in their journals “4 fives equals 20” as a multiplication sentence. Students will share their answers with their neighbor. Students will compare the addition sentence to the multiplication sentence in their journals by using the sentence starter, “I can show the answer to “4 fives equals 20” in two ways.”
4. Students will write their own repeated addition sentence in their journal. Students will share their problem with their partner and have their partner demonstrate the sentence using equal groups (drawing or manipulatives). Students will then write the multiplication sentence next to the addition sentence in their journal.
Plans for Informal Assessment:
Teacher will make notes of how students explain their answers and strategies to each other. Teacher will review journal entries to see if they understand the concept of equal groups.
Teacher will end the lesson by bringing the whole class together and asking students to respond to the essential questions of the lesson:
• How can you solve the same problem using repeated addition and multiplication?
• How are multiplication sentences and addition sentences the same? How are they different?
• How are equal sized groups connected to multiplication?
Teacher will then ask for the group to give a thumbs up, thumbs down, or an “in-between” thumb to show their comfort level with equal groups.
All right. Kudos to you if you made it all the way through this one! I was really happy with my grade on this lesson, and I feel like it is ready to be used in the classroom as it is now. Next week, I’ll be teaching a lesson in my student teaching class. I can’t wait to share how it goes! Have a good week everyone!!
I am particularly proud of a recent lesson plan I wrote with my classmate Gabby White. It’s a second grade math lesson on investigating multiplication. It’s a pretty good sample …