MD-Geometric+measurement-understand+concepts+of+area+&+relate+area+to+multiplication+&+to+addition

3.MD.5.Recognize area as an attribute of plane figures and understand concepts of area measurement. a. A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area. b. A plane figure which can be covered without gaps or overlaps by //n// unit squares is said to have an area of //n// square units. 3.MD.6. Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). 3.MD.7.Relate area to the operations of multiplication and addition. a. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. b. Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. c. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths //a// and //b// + //c// is the sum of //a// × //b// and //a// × //c//. Use area models to represent the distributive property in mathematical reasoning. d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems. || ===‍‍‍‍‍‍**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**===
 * Geometric measurement: understand concepts of area and relate area to multiplication and to addition.**
 * 3.MD.5 a/b 3.MD.6 3.MD.7 a/b/c/d**
 * ===‍‍‍‍‍‍**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 explain ideas or concepts, construct meaning from instructional messages, including oral, written, and graphic communication? (Interpreting, summarizing, paraphrasing, classifying, explaining, exemplifying, inferring, comparing) 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.MD.5 a/b Understanding**
 * 3.MD.6 3.MD.7 a/b/c/d Applying **

‍‍‍‍‍‍**I can...**

 * 3.MD.5 a/b I can explore the concept of covering a region with unit squares with no gaps or overlapping. **
 * Describe area as an attribute of plane figures.
 * Identify a square with the side length of 1 unit as a unit square.
 * Demonstrate that area can be measured by covering a surface with unit squares with no gaps or overlaps.
 * A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.


 * 3.MD.6 I can c ount unit squares to determine area of a plane figure. **
 * Cover a region with unit squares (without gaps or overlaps) and count to determine the area of a surface.
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Shade in unit squares (without gaps or overlaps) on grid paper and label to represent the area of a surface in m, cm, in, and ft.
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).


 * <span style="font-family: Arial,sans-serif;">3.MD.7 a/b/c/d I can s <span style="font-family: Arial,sans-serif; font-size: 10pt;">how the relationship between tiling a rectangle and multiplying the side lengths to find area of a plane figure. Solve real world problems by using area models to represent distributive property. **
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Model the concept of multiplication by tiling a rectangle and finding the area.
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Represent a whole number as rectangular areas, using graph paper (e.g., 12 can be represented by a 1x12, 2x6, 3x4, 4x3, 6x2, and 12x1 rectangle).
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Model the distributive property of multiplication over addition using area models by tiling rectangles in more than one way (see unpacking).
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Apply the distributive property of multiplication over addition as a problem solving strategy.
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Decompose rectilinear figures into non-overlapping rectangles; find the areas of each rectangle to determine the area of the rectilinear figure.

<span style="font-family: Arial,sans-serif; font-size: 10pt;">Example: 4 x 2 = 8 <span style="font-family: Arial,sans-serif; font-size: 10pt;">2 x 2 =40 <span style="font-family: Arial,sans-serif; font-size: 10pt;">8 + 4 = 12 <span style="font-family: Arial,sans-serif; font-size: 10pt;">area of the figure is 12 units


 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Determine the relationship between multiplication and addition by solving area problems using each operation.
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Solve real world problems involving area models and rectilinear figures.
 * <span style="font-family: Arial,sans-serif; font-size: 10pt;">Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. Multiply side lengths to find areas of rectangles with whole- number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.

‍‍‍‍‍‍**Essential Vocabulary**
Teacher Glossary

‍‍‍‍‍‍**Sample Assessments** ‍‍‍‍‍‍**Differentiation**
 * 3.MD.5 a/b || 3.MD.6 || 3.MD.7 a/b/c/d ||
 * **<span style="font-family: Arial,sans-serif; font-size: 10pt;">Attribute ** **<span style="font-family: Arial,sans-serif; font-size: 10pt;">Area ** **<span style="font-family: Arial,sans-serif; font-size: 10pt;">Square unit ** **<span style="font-family: Arial,sans-serif; font-size: 10pt;">Plane figure ** **<span style="font-family: Arial,sans-serif; font-size: 10pt;">Gap ** **<span style="font-family: Arial,sans-serif; font-size: 10pt;">Overlap ** **<span style="font-family: Arial,sans-serif; font-size: 10pt;">Square cm ** **<span style="font-family: Arial,sans-serif; font-size: 10pt;">Square m ** **<span style="font-family: Arial,sans-serif; font-size: 10pt;">Square inch ** **<span style="font-family: Arial,sans-serif; font-size: 10pt;">Square feet ** <span style="font-family: Arial,sans-serif; font-size: 10pt;">Non standard unit **<span style="font-family: Arial,sans-serif; font-size: 10pt;">Tiling ** **<span style="font-family: Arial,sans-serif; font-size: 10pt;">Side length ** **<span style="font-family: Arial,sans-serif; font-size: 10pt;">Decomposing ** || **<span style="font-family: Arial,sans-serif; font-size: 10pt;">Unit square ** **<span style="font-family: Arial,sans-serif; font-size: 10pt;">Area ** **<span style="font-family: Arial,sans-serif; font-size: 10pt;">Gap ** **<span style="font-family: Arial,sans-serif; font-size: 10pt;">Overlap ** **<span style="font-family: Arial,sans-serif; font-size: 10pt;">Tiling ** **<span style="font-family: Arial,sans-serif; font-size: 10pt;">Square inch ** **<span style="font-family: Arial,sans-serif; font-size: 10pt;">Square feet ** <span style="font-family: Arial,sans-serif; font-size: 10pt;">Square centimeter  **<span style="font-family: Arial,sans-serif; font-size: 10pt;">Square meter ** || **<span style="font-family: Arial,sans-serif; font-size: 10pt;">Area ** <span style="font-family: Arial,sans-serif; font-size: 10pt;">Distributive property  **<span style="font-family: Arial,sans-serif; font-size: 10pt;">Rectilinear ** **<span style="font-family: Arial,sans-serif; font-size: 10pt;">Tiling ** **<span style="font-family: Arial,sans-serif; font-size: 10pt;">Overlapping ** **<span style="font-family: Arial,sans-serif; font-size: 10pt;">Non overlapping ** **<span style="font-family: Arial,sans-serif; font-size: 10pt;">Decomposing ** **<span style="font-family: Arial,sans-serif; font-size: 10pt;">Polygon ** **<span style="font-family: Arial,sans-serif; font-size: 10pt;">Square unit ** ||
 * **Formal and informal teacher made assessments using RBT question stems.**
 * **District predictive assessments.**
 * **Standardized tests.**
 * **Observations, data collection (student data books), and conferences.**
 * **Scholastic Math Inventory**
 * 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**
 * 10) Illuminations site

‍‍‍‍‍‍**Intervention:**
‍‍‍‍‍‍**Enrichment:**
 * 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.comwww.mathplayground.com**
 * **Intervention sites**: (JennyLendElementary) www.mathwire.com
 * **Investigations Math site**
 * **Illuminations site**
 * 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) **Illuminations site**

‍‍‍‍‍‍**Instructional Resources** === Envisions Math Student pages 3.MD.7a 3.MD.7d 3.MD.7c === Investigations Math Websites Manipulatives (hands-on instruction) graphing paper of various sizes multiplication bars