OA-Solve+problems+involving+the+four+operations,+&+identify+&+explain+patterns+in+arithmetic

3.OA.8. Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.* 3.OA.9. Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. //For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.// //*//This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order. || ===‍‍‍‍‍‍**Anchor Standard/Mathematical Practice(s)**=== 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||
 * ===**Common Core Standards**===
 * Solve problems involving the four operations, and identify and explain patterns in arithmetic.**
 * 3.OA.8/3.OA.9**
 * ===‍‍‍‍‍‍**Information Technology Standard**===

**3.TT.1 Use technology tools and skills to reinforce classroom concepts and activities.**
|| ===‍‍‍‍‍‍**Revised Bloom's Level of thinking**=== Can the student break information into arts to explore understandings and relationships? (Comparing, Organizing, Deconstructing, Interrogating, Finding, Differentiating, Attributing)
 * 3.OA.8 Analyzing**
 * 3.OA.9 Evaluating ** Can the student justify a decision or course of action or make judgments based on a criteria or a standard? (checking, hypothesizing, critiquing, experimenting, and judging.) ||

‍‍‍‍‍‍**I can...**
I can solve two-step problems that include an unknown using various strategies (e.g. estimating, rounding, check for reasonableness). I can identify and explain arithmetic patterns by using properties of operations.
 * 3.OA.8**
 * Identify strategies for determining important information within a word problem.
 * Model the mathematics within one-step word problems using objects or pictures.
 * Determine the equation that represents the mathematics within a one-step word problem using a letter for the unknown value.
 * Solve equations with a letter for the unknown quantity in one-step word problems.
 * Model the mathematics within two-step word problems using objects or pictures.
 * Determine the equation that represents the mathematics within a two-step word problem using a letter for the unknown value.
 * <span style="font-family: Arial,sans-serif;">Solve equations with a letter for the unknown quantity in two-step word problems.
 * <span style="font-family: Arial,sans-serif;">Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
 * <span style="font-family: Arial,sans-serif;">Model strategies of using the important information to solve one and two-step word problems using the four operations
 * <span style="font-family: Arial,sans-serif;">Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
 * <span style="font-family: Arial,sans-serif;">3.OA.9 **
 * Identify arithmetic patterns involving both addition and multiplication (e.g., //3, 6, 9, 12// is an arithmetic pattern that increases by 3).
 * Identify arithmetic patterns on addition tables and multiplication charts
 * Extend arithmetic patterns using a variety of strategies and tools (e.g., addition tables, multiplication charts, calculators, and student generated tables/t-charts)
 * Make and test conjectures about arithmetic patterns (e.g., 4 times a number is always even; the product of 4 times a number can always be broken into two equal quantities)
 * Explain why specific arithmetic patterns occur using properties of operations (e.g., use distributive property to explain why even numbers can always be composed of two equal addends).
 * Find and use patterns to solve problems.

‍‍‍‍‍‍**Essential Vocabulary**
Teacher Glossary <span style="font-family: Arial,sans-serif; font-size: 10pt;">Multiply <span style="font-family: Arial,sans-serif; font-size: 10pt;">Divide <span style="font-family: Arial,sans-serif; font-size: 10pt;">Factor <span style="font-family: Arial,sans-serif; font-size: 10pt;">Product <span style="font-family: Arial,sans-serif; font-size: 10pt;">Quotient <span style="font-family: Arial,sans-serif; font-size: 10pt;">Subtract <span style="font-family: Arial,sans-serif; font-size: 10pt;">Add <span style="font-family: Arial,sans-serif; font-size: 10pt;">Addend <span style="font-family: Arial,sans-serif; font-size: 10pt;">Sum <span style="font-family: Arial,sans-serif; font-size: 10pt;">Difference <span style="font-family: Arial,sans-serif; font-size: 10pt;">Equation <span style="font-family: Arial,sans-serif; font-size: 10pt;">Variable <span style="font-family: Arial,sans-serif; font-size: 10pt;">Unknown <span style="font-family: Arial,sans-serif; font-size: 10pt;">Strategies <span style="font-family: Arial,sans-serif; font-size: 10pt;">Reasonableness <span style="font-family: Arial,sans-serif; font-size: 10pt;">Mental computation <span style="font-family: Arial,sans-serif; font-size: 10pt;">Estimation <span style="font-family: Arial,sans-serif; font-size: 10pt;">Rounding <span style="font-family: Arial,sans-serif; font-size: 10pt;">Patterns <span style="font-family: Arial,sans-serif; font-size: 10pt;">Properties || <span style="font-family: Arial,sans-serif; font-size: 10pt;">Addends <span style="font-family: Arial,sans-serif; font-size: 10pt;">Multiples <span style="font-family: Arial,sans-serif; font-size: 10pt;">Patterns <span style="font-family: Arial,sans-serif; font-size: 10pt;">Decomposing <span style="font-family: Arial,sans-serif; font-size: 10pt;">Factors <span style="font-family: Arial,sans-serif; font-size: 10pt;">Properties of operations <span style="font-family: Arial,sans-serif; font-size: 10pt;">Tables ||
 * **3.OA.8** || **3.OA.9** ||
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Operation

‍‍‍‍‍‍**Sample Assessments**

 * 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**
 * 6) **Thinkgate.net**

‍‍‍‍‍‍**Differentiation**

 * 1) ** Learning style surveys (student interest and teacher created). **
 * 2) ** Small group settings based on skill levels. **
 * 3) ** Peer tutors. **
 * 4) ** Tiered assignments. **
 * 5) ** Flexible grouping **
 * 6) ** Centers (finding, identifying, creating patterns with numbers, week by week essentials games) **
 * 7) **Learning Contracts**
 * 8) **Choice boards (create math games, make flashcards)**
 * 9) **Investigations website**

‍‍‍‍‍‍**Intervention:**

 * **Scholastic Math Inventory**
 * **Math Tutors**
 * **One on one direct instruction**
 * **Math based web sites ([|www.multiplication.com], [|www.abcya.com], [|www.ixl.com], [|www.sheppardssoftware.com]www.mrsgoldsclass.com www.mathplayground.com**
 * **Intervention sites**: (JennyLendElementary) www.mathwire.com
 * ** Investigations Math site **
 * ** Illuminations site **

‍‍‍‍‍‍**Enrichment:**
 * 1) **Math based web sites ([|www.multiplication.com],[| www.abcya.com], [|www.ixl.com], [|www.sheppardssoftware.com])**
 * 2) **Scholastic Math Inventory**
 * 3) **Group projects (creating games, make flashcards, pose questions)**
 * 4) **Investigations Math site**

Envisions Math
Investigations Math Websites Manipulatives (hands-on instruction) base ten blocks, counters, balance scales, number lines, graph paper of various designs