Roslynn Sampson CCLM Project 2
July 15, 2011
CCSSM Interpretation Guide
Parts 1 and 2 The standards I will be using come from third grade Operations and Algebraic Thinking. 3OA.1 Interpret products of whole numbers, e.g. interpret 5 x 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 x 7. The standard is in teacher and student friendly language. Students will be learning to multiply. Multiplication is about adding equal groups. They will provide a context for multiplication of facts. e.g. 4 x 6 xxxxxx xxxxxx xxxxxx xxxxxx or 4 + 4+ 4+ 4 + 4 + 4 Teachers will explain that in the first example, there are 4 groups with 6 objects in each group. In the second example, the student is showing that the same answer can be reached by adding 4, 6 times. Either one is representation of 4 x 6. There are no new terms that teachers will need to introduce. They will simple have to remind students that the numbers that are being multiplied are called factors and the answer is called the product. DRAFT DOCUMENT, UNEDITED COPY. This material was developed for the Common Core Leadership in Mathematics (CCLM) project at the University of Wisconsin-­‐Milwaukee. (07.15.2011) The next standard is 3OA.2. This standard wants students to: Interpret whole-­‐number quotients of numbers, e.g. interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 object each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. This standard, just like OA.1 is in teacher and student friendly terms. Students will learn how to partition objects into equal shares. Partitioning means to divide objects into equal size parts. They will develop the skills and strategies needed to partition successfully while finding unknown factors. e.g. 15 ÷ 3 = 5 J J J J J J J J J J J J J J J or 15 – 3 = 12 12 – 3 = 9 9 – 3 = 6 6 – 3 = 3 3 – 3 = 0 In the first example teachers will explain that 15 is the total number of items 3 is the number of equal groups the 5 represents the number in each group. The second example is known as repeated subtraction. Repeated can be shown as it is above or a number line can be used to. The number line would begin at 0 and end at 15. The teacher would show how to make 3 equal groups that covered 5 numbers at a time. DRAFT DOCUMENT, UNEDITED COPY. This material was developed for the Common Core Leadership in Mathematics (CCLM) project at the University of Wisconsin-­‐Milwaukee. (07.15.2011) Part 3 Textbook Development for 3OA.1: Scott Foresman n Addison Wesley (SFAW) introduces Multiplication Concepts and Facts as repeated addition or joining equal groups. This is done in twelve lessons that introduce students to vocabulary, how to write multiplication sentences and stories, the difference between 5 groups with 7 objects and 7 groups with 5 objects, how to use arrays and how to do multi step problems word problems. The students will be using skills that they were taught in second grade. The vocabulary for this chapter is: multiplication – is putting together the total number of equal groups factor -­‐ Numbers that are multiplied together to give a product. 5 x 7 = 35 á á (The arrows are under the factors.) product-­‐ the answer to a multiplication problem array-­‐ away of displaying objects in rows and columns Commutative (order) Property of Multiplication – numbers can be multiplied in any order and the product will be the same. 5 x 7 = 35 7 x 5 = 35 multiple-­‐ the product of the number and any other whole number 0, 4,8,12 and 16 are multiples of 4 even number-­‐a whole number that has 0, 2, 4, 6,0r 8 in the ones place; A number that is a multiple of 2. Identity (one) Property of Multiplication-­‐The product of any number and 1 is that same number. 1 x 8 = 8 Zero Property of Multiplication-­‐ The product of any number and zero is zero. 0 x 10 = 0 DRAFT DOCUMENT, UNEDITED COPY. This material was developed for the Common Core Leadership in Mathematics (CCLM) project at the University of Wisconsin-­‐Milwaukee. (07.15.2011) The students were taught the concept of repeated addition, skip counting on a number line and how to make and use arrays in second grade. Once they have completed this chapter, the skills will be used again in Chapter 6 and then again in fourth grade when students will review multiplication concepts to help them write evaluating multiplication expression. The skill will be developed by using concepts and strategies for learning basic multiplication facts with factors 2,5,9 and 10 while using the multiplication properties of identity, zero and commutative. Students reviewed the commutative and associative properties in Chapter 2. Hopefully, the students will be able to use those skills when learning the multiplication properties. Conclusion: SFAW will be able to meet the standard for grade three OA.1. There are plenty of activities that support what the standard wants the students to learn. There are different strategies that teachers will be able to use to teach the concepts. Suggestions: Teachers will be more successful if they plan the unit by using all parts of the Lesson Planner as well as the Investigation piece instead of going right to the first student page. Using the Lesson Planner helps the teacher see not only what the students should learn, but how the students will learn best. It is filled with ideas, the background of the unit, what the students should already know, when they were taught skills, and gives examples of how skills were taught. There is also a Literature connection that is a nice touch that could be used in a Math Station or as another way to get the students to understand the concepts. Textbook Development for 3OA.2 SFAW introduces Division Concepts and Facts by defining what it means to divide. The series defines it as repeated subtraction and sharing. Students are encouraged to try to relate a multiplication fact e.g. 7 x 6 = 42, 6 x 7 =42, 42 ÷ 7 = 6, and 42 ÷ 6 = 7. Depending on what is happening in the world around the students, they will either look at division as a repeated subtraction problem (e.g. can be found on page 2, 15 ÷ 3) or they will look at it as sharing problem e.g. 42 divided by 7 equal groups. SFAW also uses Try, check and revise. This strategy has 4 steps to it. Step I Make a reasonable first try. Step 2 Check using data given in the problem. Step 3 Revise. Use your first try to make a reasonable second try. Step 4 Continue trying and checking until you get the answer. DRAFT DOCUMENT, UNEDITED COPY. This material was developed for the Common Core Leadership in Mathematics (CCLM) project at the University of Wisconsin-­‐Milwaukee. (07.15.2011) The strategies that are used to teach division have been used in second grade and earlier in third grade. Because of this, students get more practice with using a particular strategy that they are able to make for them all of the time. If they are not able to find one, that is okay because there is more practice in chapter eleven when the same strategies are used to teach how to divide a two digit by a one digit number and again in fourth grade when there will be a review of division concepts. Conclusions: SFAW uses the terms repeated subtraction and sharing when teaching division. With those terms come different strategies to help students get a firm understanding of the concept. The standard focuses on two models. These models are partition and measurement, which is repeated subtraction. Because of this, teachers should have no problem with this standard. They will have to teach repeated subtraction using a number line as well as showing it as a number sentence. Teachers will have to use the term “partition equally” instead of “sharing equally”. Suggestions: Teachers will need to get use to suing the vocabulary that the standard uses. Once teaches use it regularly, their students will be able to use it regularly. I believe here just like with 3OA.1 those teachers will be more successful if they plan the unit by using all parts of the Lesson Planner as well as the Investigation piece instead of going right to the first student page. Using the Lesson Planner helps the teacher see not only what the students should learn, but how the students will learn best. It is filled with ideas, the background of the unit, what the students should already know, when they were taught skills, and gives examples of how skills were taught. There is also a Literature connection that is a nice touch that could be used in a Math Station or as another way to get the students to understand the concepts. DRAFT DOCUMENT, UNEDITED COPY. This material was developed for the Common Core Leadership in Mathematics (CCLM) project at the University of Wisconsin-­‐Milwaukee. (07.15.2011) Part 4 “Check Point” Formative Assessment Task that Reveals Student Thinking The formative assessment task for 3OA.1 Which are other names for 7 x 8? Students will be given choices. They will have to explain why they choose their answers. I hope to see that the students use repeated addition or joining equal groups. They will have to show that there are 7 groups that contain 8 objects. A blank copy of this assessment is on page seven of this document. Page eight will have an example of proficient student work with and explanation of what the student did. The formative assessment task for 3OA.2 A classroom has 24 books. If the teacher gives each student 3 books, how many students will get books?
Students will have to explain their answer. I would hope to see that the students use partitioning into equal groups or that they use the repeated subtractions using a number line or a subtraction sentence. A blank copy of this assessment is on page nine of this document. Page ten will have an example of proficient student work with and explanation of what the student did. DRAFT DOCUMENT, UNEDITED COPY. This material was developed for the Common Core Leadership in Mathematics (CCLM) project at the University of Wisconsin-­‐Milwaukee. (07.15.2011) Name ___________________________ Which are other names for 7 x 8? Mark all the correct answers. o 7 + 8 o 56 o 8 + 8 + 8 + 8 + 7 + 7 + 7 + 7 o 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 o 8 x 7 o 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 Show how you know your answers are correct. Use pictures and or words. DRAFT DOCUMENT, UNEDITED COPY. This material was developed for the Common Core Leadership in Mathematics (CCLM) project at the University of Wisconsin-­‐Milwaukee. (07.15.2011) The student chose the correct answers and explained the work using equal groups and repeated addition. DRAFT DOCUMENT, UNEDITED COPY. This material was developed for the Common Core Leadership in Mathematics (CCLM) project at the University of Wisconsin-­‐Milwaukee. (07.15.2011) Name _______________________________
A classroom has 24 books. If the teacher gives each student 3 books, how many students will get books?
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Show how you know your answer is correct. Use words and or pictures. ¡ 21
¡ 8
¡ 9
DRAFT DOCUMENT, UNEDITED COPY. This material was developed for the Common Core Leadership in Mathematics (CCLM) project at the University of Wisconsin-­‐Milwaukee. (07.15.2011) The student partitioned using tally marks to show that there are 8 groups with 3 tally marks in each group. DRAFT DOCUMENT, UNEDITED COPY. This material was developed for the Common Core Leadership in Mathematics (CCLM) project at the University of Wisconsin-­‐Milwaukee. (07.15.2011)