NCEA Math Lesson Plan Grade: 3 Subject: Mathematics Domain: Operations and Algebraic Thinking Standard Number(s) and Description: 3.OA.1 Interpret products of whole numbers as the total number of objects in groups with the same number in each. 3.OA.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities. 3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers. Vocabulary to be Highlighted: Equal groups, product Mathematical Practices (#): 1. Make sense of problems and persevere in solving them. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 6. Attend to precision. Essential Questions: What is the meaning of the calculations that are being done, in terms of the context with which we began? If we do not know the answer immediately, what can we do to use the mathematics we know to get to the answer? Are my classmate solving this the same way I am? Can I prove that my answer is correct? Are my classmates solving our problem correctly? How are their methods related to mine? How does this relate to real world experiences you have had? How do two different and unrelated situations lead us to the same mathematics while solving? Can we solve the problem another way to be sure that we know we're correct? Materials/Tools (include technology): Whiteboard Chart paper Sentence strips Snap cubes Connections to Other Math Domains: In solving, a connection can be made to geometry if the class chooses to use arrays to represent the situations. Geometric figures are a context where groups are seen, in terms of numbers of sides and angles. Some number combinations will lean on and further students' knowledge of the base ten structure. Connections to Other Subject Areas: Many things come in groups, so the teacher can point to examples in almost any discipline, including physical education, religion, health, science, literature, or social studies. Word problems created by the teacher could relate to not only the brainstorming of the class about groups, but include questions related to ongoing lessons in another class or from a field trip. Catholic Identity Component: Students will be practicing interpersonal skills while brainstorming, such as active listening, respect for others' ideas, taking turns, making effort to contribute to move work forward. Generated lists and problems, as mentioned above, may include religious themes. Examples are below. Resources (attachments): Most ideas are meant to come from the students with the guidance of the teacher, but the teacher may research more difficult group numbers ahead of time (on the internet) in order to be ready to assist students. Snap cubes could be available to help students model the situations. Activities/Timeline: Whole class on carpet or in seats: 1. Students can begin the class with an activity such as “What's the question?” where the teacher writes a number on the board, for instance, 20. Then the teacher states. “20 is the answer. What's the question?” and records student responses, in words or mathematical symbols. A short discussion about how some answer may be related, or highlighting and correcting any wrong responses is in order. 2. Next the teacher presents the title “Things That Come in Groups.” This could be on the top of chart paper which lists the numbers from 2-12 with space between, or on the board with sentence strips, one each for the numbers 2-12. Explain to the students that they will be brainstorming things that occur in each of the numbers given. (This could be given as a homework assignment for the week prior to this lesson, in order that students would be able to seek out examples in the grocery store, etc., rather than off the tops of their heads.) 3. If there is time, groups may be assigned to consider each number. The numbers 7 and 11 usually elicit fewer easy responses, so keep that in mind when assigning numbers. Give each group 4 numbers to do. The number assignments can overlap. 4. Next, the teacher begins taking and recording responses. The numbers do not have to be addressed in order; rather, students can contribute an idea that fits any given number, and this tends to encourage more responses from a wider variety of students. As numbers fill, encourage students to consider the numbers that have the fewest ideas listed. If some numbers are blank or have only one response, that number can be left as a homework idea, or be filled in during the day if a student comes up with an idea. (Leave the groups page posted in the classroom.) Ideas should be things that apply to all the students (i.e., avoid naming particular numbers of siblings in a family, etc., unless a student wants their family used for a difficult number such as 7 or 11). Some ideas may be: 2- eyes, feet, hands, disciples sent to evangelize by Jesus in pairs, animals on the ark, shoes, bike tires, light bulbs, peanut butter cups 3- persons in the Trinity, people in the Holy Family, sides of a triangle, toes on a chicken, the disciples Jesus took with him most often, number of loaves that fed the multitude, multipack bottles of bubbles, wise men, little pigs, tricycle wheels, clover leaves, meals per day 4- sides/vertices of a rectangle, directions (NSEW), ends of a cross, limbs, feet on many animals, corners in a rectangular room, car wheels, bases, KitKats 5- fingers, weekdays, basketball team, points on a star, oceans, starfish legs 6- pack of soda, insect legs, sides on a die, guitar strings, star of David points 7- sacraments, days it took to create the earth, gifts of the Holy Spirit, dwarves, days of the week, times to forgive (times 70), colors in the rainbow, Quidditch team, continents 8- Beatitudes, spider/octopus legs, hot dogs, hamburger buns, corners on a cube, pack of V-8 cans, sides on a stop sign 9-reindeer (need Rudolph), cat's lives, baseball team 10-Commandments, plagues in Egypt, fingers/toes, packs of gum, dimes in a dollar, cents in a dime 11-soccer team, football team 12- fruits of the Holy Spirit, eggs, case of soda, Apostles, hours in the day/night, months, frozen burgers, popsicles Lesson 2 Small group or individual work (prepare in whole group): Next the teacher models how to use the ideas generated to create word problems about the things that come in groups. Choose from the ideas on the sheets, but let the students know that when they break to work, they can use new ideas as well, and those can be added to the sheets. You can choose to solve the sample questions, or not, but the student-generated questions should be solved by them so that they can lead discussion about them at a later time. Ex: In the first hour, 10 pairs of animals boarded Noah's Ark. How many animals boarded? Ex: I am knitting footies for my six dogs. How many footies do I need to knit? Ex: Jesus gave each Apostle three loaves of bread. How many loaves of bread in all? Students work together (recommended) or alone to design 5 questions of their own and solve them. They should all agree on the solution, and if time permits, think about a second way to solve each. Alternatively, assigning each student to design and solve one or two problems could be homework. Lesson 3 Class gathers in whole group to share and solve problems. A good model is think/pair/share among those who are working to solve. If students are mature enough, the presenting group can play teacher and walk around to look at work and decide whom to call on. Make the connection to the number sentence for each problem solved. Take time to ask students to create a problem that fits a certain number sentence. Formative Assessment (what to look for, how/when to look): While brainstorming, watch that students are observing proper classroom norms. Look for students to present ideas that are constantly in that size group. Understanding the constancy of the number in a group is critical to multiplication. In designing questions, look to see that students are using the groups correctly, that the contexts are such that equal groups are used a discrete number of times. Students should not design questions where each member of a group gets a differing amount of something, or where a group member could be left out. Watch for students who have good understanding to combine examples (i.e., number of feet of the Apostles). Most students will begin to solve using repeated addition. Look to see that they organize their work so as not to forget an addend. Look to see a progression from adding single numbers to grouping by twos and by tens, possibly by threes. Encourage students to group groups (i.e., add groups of two, and then add these answers two at a time). Make note if students have some fact fluency, and use these later to build to the facts they need to learn. Summative Assessment: Have students create a problem that fits a given number sentence, and solve. Give students a few problems that elicit information about their fact fluency and base 10 knowledge: one that uses pairs (x2), one that uses 5s, and one that uses 10s, and another that uses a less accessible number to see what their strategies look like for that.