enVision Mathematics Topic 6
3rd Grade; October – November (3 weeks); 1st/2nd Trimester
Embedded Files
Topic Title(s):
Connect Area to Multiplication and Addition
Prepared Graduates:
MP3. Construct viable arguments and critique the reasoning of others.
MP5. Use appropriate tools strategically.
MP6. Attend to precision.
MP7. Look for and make use of structure.
Standard(s):
3. Data, Statistics, and Probability
The highlighted evidence outcomes are the priority for all students, serving as the essential concepts and skills. It is recommended that the remaining evidence outcomes listed be addressed as time allows, representing the full breadth of the curriculum.
Students Can (Evidence Outcomes):
3.MD.C. Measurement & Data: Geometric measurement: Use concepts of area and relate area to multiplication and to addition.
Recognize area as an attribute of plane figures and understand concepts of area measurement. (CCSS: 3.MD.C.5)
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. (CCSS: 3.MD.C.5.a)
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. (CCSS: 3.MD.C.5.b)
Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). (CCSS: 3.MD.C.6)
Use concepts of area and relate area to the operations of multiplication and addition. (CCSS: 3.MD.C.7)
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. (CCSS: 3.MD.C.7.a)
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. (see Appendix: Table 2) (CCSS: 3.MD.C.7.b)
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. (CCSS: 3.MD.C.7.c)
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. (CCSS: 3.MD.C.7.d)
Defend calculations of area using multiplication and by tiling the area with square units and comparing the results. (MP3)
Understand how to use a one-dimensional measurement tool, like a ruler, to make two-dimensional measurements of area. (MP5)
Be precise by describing area in square rather than linear units. (MP6)
Use areas of rectangles to exhibit the structure of the distributive property. (MP7)
Inquiry Questions
Given three pictures of different rectangles with unknown dimensions, how can you determine which rectangle covers the most area?
How does computing the area of a rectangle relate to closed arrays?
How can the area of an E-shaped or H-shaped figure be calculated?
Coherence Connections
This expectation represents major work of the grade.
In Grade 2, students measure and estimate lengths in standard units and reason with shapes and their attributes.
This expectation connects to other ideas in Grade 3: (a) recognizing perimeter as an attribute of plane figures and distinguishing between linear and area measures, (b) applying properties of multiplication and the relationship between multiplication and division, and (c) solving problems involving the four operations and identifying and explaining patterns in arithmetic.
In Grade 4, students solve problems involving measurement and conversion of measurement from a larger unit to a smaller unit. In Grade 5, students relate volume to multiplication and to addition and also extend previous understandings of multiplication and division to multiply and divide fractions.
Academic Vocabulary & Language Expectations:
Area, unit square, square unit, estimate
Assessments:
Instructional Resources & Notes:
enVision Mathematics Topic 6
Additional enVision Mathematics Resources
Let's Investigate! Flag Designs (TE) (supports Lessons 6-2, 6-3, 6-4)
Tier 1 Intervention & Supports (i-Ready Tools for Instruction):
Tier 1 Intervention: Finding Area, Multiply to Find Area, Add Areas
Coherence Map/Concept Progressions: 3.MD.C.6, 3.MD.C.7.b
Page updated
Report abuse