Standard: MACC.3.OA.1.1 Depth of Knowledge Interpret products of ...

Standard: MACC.3.OA.1.1Depth of KnowledgeInterpret products of whole numbers, e.g., interpret 5 x 7 as the Level 1: Recalltotal number of objects in 5 groups of 7 objects each. Forexample, describe a context in which a total number of objects canbe expressed as 5 x 7.Explanations and Ideas to Support:Sample Test Item(s):This standard interprets products of whole numbers.Students recognize multiplication as a means to determinethe total number of objects when there are a specificnumber of groups with the same number of objects ineach group. Multiplication requires students to think interms of groups of things rather than individual things.Multiplication is seen as “groups of” and problems such as5 x 7 refer to 5 groups of 7. However, it is important forteachers to understand there are several ways in whichwe can think of multiplication:1. Multiplication is often thought of as repeatedaddition of equal groups. This concept is relatedto partitioning (which, in turn, is related todivision).2. A second concept of multiplication is that of rateor price.3. A third concept of multiplication is that ofmultiplicative comparison.Ideas to support MACC.3.OA.1.1Students need to see the connection betweenrepeated addition and multiplication. For instance, 4+ 4 + 4 is the same as 4 x 3.Arrays are an excellent visual tool that aid instudents’ abilities to see the organization ofmultiplication. The use of arrays gives students amethod for the justification of an answer with adrawing.Use of a variety of manipulatives and technologies areimportant as well.Connections:SMPs to be Emphasized MP1- Make sense of problems andpersevere in solving them. MP4- Model with mathematics. MP7- Look for and make use of structure. MP8- Look for and express regularity inrepeated reasoningFCAT 2.0 Connections:Related NGSSS Standard(s)MA.3.A.1.1- Model multiplication and division,including problems presented in context:repeated addition, multiplicative comparison,array, how many combinations, measurement,and partitioning.Tabitha is planning a birthday party. She plansto buy party whistles for each of her guests.There are 6 whistles in each package. Tabithabuys 4 packages of whistles.Write a multiplication expression to representthe total number of whistles that Tabitha buys.Nathan paid $2 for each of the 3 books hebought at a bookstore. He can use theexpression3 X 2 to find the total amount he paid for the 3books. Which of the following is equal to3 X 2?A. 3 + 3 + 3B. 2 + 2 + 2C. 3 + 2 + 3D. 2 X 3 + 3Critical Area Critical Area 1: Developing understanding of multiplicationand division and strategies for multiplication and divisionwithin 100.3 rd Grade Related Standards: MACC.3.OA standardsFoundational Skills for 4 th Grade: Represent and solve problems involving multiplication anddivision.FCAT 2.0 Test Item SpecificationBenchmark Clarification:Students will identify models of and/or solve problemsinvolving multiplication and/or division situations.Examples of multiplication or division models mightinclude, but are not limited to: Repeated addition: 4 bags of cookies with 8 in eachbag. How many cookies are there? (8 + 8 + 8 + 8 = 32) Multiplicative comparison: (also known as scalarmodel)Sam has 8 baseball cards. Elise has 8 times asmany. How many does Elise have?

Array: A marching band has 8 rows with 7 students ineach row. How many band members are there? Combination: How many different combinations of oneflavor of ice cream and one topping can be made from4 different flavors and 5 different toppings? Measurement: If there are 35 bugs all together andRobbie puts 5 bugs in each jar, how many jars does heneed to hold all of the bugs? Partitive: Robbie has 35 bugs and 7 jars. He will put allof the bugs in jars. If he puts the same number of bugsin each jar, how many bugs are in each jar?Other models might include: Finding number of squares (area) of wrapping paper;using rate models, e.g., traveling 6 miles each day for3 days; showing how 4 x 6 can be represented by6 + 6 + 6 + 6 or 6 x 4 can be represented by4 + 4 + 4 + 4 + 4 + 4.Content Limits: Items may include whole-number multiplicationfacts from 0 X 0 through 9 X 9 and the relateddivision facts. Items may include division problems withremainders expressed only as whole numbers.Items will not require interpretation of theremainder.Common Misconceptions:Students think a symbol (? or ) is always the place for the answer. This is especially true when theproblem is written as 15 ÷ 3 =? or 15 = x 3. Students also think that 3 ÷ 15 = 5 and 15 ÷ 3 = 5 are the sameequations. The use of models is essential in helping students eliminate this understanding. The use of asymbol to represent a number once cannot be used to represent another number in a differentproblem/situation. Presenting students with multiple situations in which they select the symbol and explainwhat it represents will counter this misconception.