OA-Represent+&+Solve+Problems+Involving+Mulitplication+&+Division

3.OA.1.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.// 3.OA.2. Interpret whole-number quotients of whole 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 objects each. //For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.// 3.OA.3. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.* 3.OA.4. Determine the unknown whole number in a multiplication or division equation relating three whole numbers. //For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = _ ÷ 3, 6 × 6 = ?// //*//See Glossary, Table 2. || ===‍‍‍‍‍‍**Anchor Standard/Mathematical Practice(s)**=== Represent and solve problems involving multiplication and division. 1. Make sense of problems and persevere in solving them. 4. Model with mathematics. 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 4. Model with mathematics. 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 4. Model with mathematics. 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 4. Model with mathematics. 7. Look for and make use of structure. || Can the student use information in another familiar situation; carry out or use a procedure in a given situation? (Implementing, carrying out, using, executing) Can the student break information into arts to explore understandings and relationships? (Comparing, Organizing, Deconstructing, Interrogating, Finding, Differentiating, Attributing) Can the student break information into arts to explore understandings and relationships? (Comparing, Organizing, Deconstructing, Interrogating, Finding, Differentiating, Attributing) ||
 * ===**Common Core Standards**===
 * 3.OA.1**
 * 3.OA.2**
 * 3.OA.3 **
 * 3.OA.4**
 * ===‍‍‍‍‍‍**Information Technology Standard 3.TT.1 Use technology tools and skills to reinforce classroom concepts and activities.**=== || ===‍‍‍‍‍‍**Revised Bloom's Level of thinking**===
 * 3.OA.1 Applying** Can the student use information in another familiar situation; carry out or use a procedure in a given situation? (Implementing, carrying out, using, executing)
 * 3.OA.2 Applying**
 * 3.OA.3 Analyzing**
 * 3.OA.4 Analyzing**

‍‍‍‍‍‍**I can...**

 * 3.OA.1 I can recognize the first factor in a multiplication problem as the number of groups and the second factor as the number in each group. **
 * Identify explicit vocabulary words for multiplication.
 * Recognize multiplication as repeated addition.
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Design visual representation of multiplication models (arrays, groups).
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Generate and compute both horizontal and vertical multiplication problems.
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Interpret a problem situation requiring multiplication using pictures, objects, words, numbers, and equations for single-digit factors.
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7.


 * <span style="font-family: Arial,sans-serif;">3.OA.2 I can u <span style="font-family: Arial,sans-serif; font-size: 10pt;">se models to interpret whole-number quotients as partition models or repeated subtraction. **
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Identify explicit vocabulary words for division.
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Recognize division as repeated subtraction.
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Recognize the operation of division in two different types of situations. One situation requires determining how many groups and the other situation requires sharing (determining how many in each group).
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Design visual representation of division models (arrays, groups).
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Interpret a problem situation requiring division using pictures, objects, words, numbers, and equations for single-digit factors.
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Interpret whole-number quotients of whole 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 objects each.


 * <span style="font-family: Arial,sans-serif;">3.OA.3 I can a <span style="font-family: Arial,sans-serif; font-size: 10pt;">pply various strategies to solve word problems involving multiplication and division problems within 100. **
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Represent a problem situation involving equal groups, arrays, and measurement quantities, with a multiplication or division expression.
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Use pictures, numbers or words to solve for the unknown within word problems.
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Solve single and multi-digit word problems using a variety of multiplication and division strategies.
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities.


 * <span style="font-family: Arial,sans-serif;">3.OA.4 I can e <span style="font-family: Arial,sans-serif; font-size: 10pt;">xplore inverse operations of multiplication and division to find the unknown number in an equation. **
 * Represent a multiplication situation with an equation, where the unknown may be a factor or the product (e.g., 3 x //b// = 12; 3 x 4 = //b//).
 * Represent a division situation with an equation, where the unknown may be the dividend, divisor, or quotient (e.g., //b// ÷ 3 = 4; 12 ÷ //b = 4; 12// ÷ 3 = //b//).
 * Describe the inverse relationship between multiplication and division.
 * Apply the inverse relationship of multiplication and division to solve problems //(e.g., I can find the unknown in the division equation „b † 3 = 4‟ by multiplying 3 times 4.)//.
 * Determine the unknown whole number in a multiplication or division equation relating three whole numbers.

‍‍‍‍‍‍**Essential Vocabulary** Teacher Glossary <span style="font-family: Arial,sans-serif; font-size: 10pt;">rectangular <span style="font-family: Arial,sans-serif; font-size: 10pt;">expression <span style="font-family: Arial,sans-serif; font-size: 10pt;">factors <span style="font-family: Arial,sans-serif; font-size: 10pt;">product <span style="font-family: Arial,sans-serif; font-size: 10pt;">multiplication <span style="font-family: Arial,sans-serif; font-size: 10pt;">multiply <span style="font-family: Arial,sans-serif; font-size: 10pt;">vertical <span style="font-family: Arial,sans-serif; font-size: 10pt;">horizontal <span style="font-family: Arial,sans-serif; font-size: 10pt;">array <span style="font-family: Arial,sans-serif; font-size: 10pt;">repeated addition <span style="font-family: Arial,sans-serif; font-size: 10pt;">fact family <span style="font-family: Arial,sans-serif; font-size: 10pt;">multiples <span style="font-family: Arial,sans-serif; font-size: 10pt;">uotient || <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">equal groups <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">unknown  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">array  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Quotient  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Dividend  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Divisor  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Factor  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Equal  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">shares  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Division  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Vertical  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Horizontal  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Symbols  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">of division  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">(/ ┌ ÷)  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">partition  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">estimate  <span style="font-family: Arial,sans-serif; font-size: 10pt;">rounding || <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Unknown   product   groups of   quotient   division   equation   multiplication   equal groups   expression  equally partitioned  factor   quotient   rectangular array  || <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Inverse  <span style="display: block; font-family: Arial,sans-serif; font-size: 10pt; text-align: center;">Unknown   product   groups of   quotient   division   equation   multiplication   equal groups   expression  equally partitioned  factor   quotient   rectangular array  <span style="font-family: Arial,sans-serif; font-size: 10pt;">symbols || ‍‍‍‍‍‍**Sample Assessments**
 * **3.OA.1** || **3.OA.2** || **3.OA.3** || **3.OA.4** ||
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">equal groups
 * 1) **Formal and informal teacher made assessments using RBT question stems.**
 * 2) **District predictive assessments.**
 * 3) **Standardized tests.**
 * 4) **Observations, data collection (student data books), and conferences.**
 * 5) **Scholastic Math Inventory**

‍‍‍‍‍‍**Differentiation**
‍**‍‍‍‍‍Intervention:**
 * 1) **Learning style surveys (student interest and teacher created).**
 * 2) **Small group settings based on skill levels.**
 * 3) **Peer tutors.**
 * 4) **Tiered assignments.**
 * 5) **Compacting lesson (moving on if students already have prior knowledge).**
 * 6) **Centers**
 * 7) **Flexible grouping (not always based on skill level).**
 * 8) **Choice boards (independent practice, choice of 2 or 3 activities of creating lessons, flashcards, creating new problems, facilitating activity for another group).**
 * 9) **Learning contracts**
 * 1) **Scholastic Math Inventory**
 * 2) **Math Tutors**
 * 3) **One on one direct instruction**
 * 4) **Math based web sites ([|www.multiplication.com], [|www.abcya.com], [|www.ixl.com], [|www.sheppardssoftware.com]www.mrsgoldsclass.com**
 * 5) **Intervention web sites** (JennyLendElementary) www.mathwire.com
 * 6) ** Investigations Math site **
 * 7) ** Illuminations site **

‍‍‍‍‍‍**Enrichment:**

 * 1) **Math based web sites ([|www.multiplication.com],[| www.abcya.com], [|www.ixl.com], [|www.sheppardssoftware.com]) www.quizlet.com**
 * 2) **Scholastic Math Inventory**
 * 3) **Group projects (creating games, make flashcards, pose questions)**
 * 4) Enrichment sites www.mathwire.com Enrichement list About.comMath

‍‍‍‍‍‍**Instructional Resources**
===Envisions Math Student pages OA3 OA 3 OA4=== Investigations Math Websites Manipulatives (hands-on instruction) playing cards multiplication bars hundreds charts counters number balance scale (can be used for multiplication)