enVision Mathematics Topics 2-5
4th Grade; September – November (10 weeks); 1st/2nd Trimester
enVision Mathematics Topics 2-5
4th Grade; September – November (10 weeks); 1st/2nd Trimester
Topic Title(s):
Fluently Add and Subtract Multi-Digit Whole Numbers (Topic 2)
Use Strategies and Properties to Multiply by 1-Digit Numbers (Topic 3)
Use Strategies and Properties to Multiply by 2-Digit Numbers (Topic 4)
Use Strategies and Properties to Divide by 1-Digit Numbers (Topic 5)
Prepared Graduates:
MP3. Construct viable arguments and critique the reasoning of others.
MP6. Attend to precision.
MP7. Look for and make use of structure.
Standard(s):
1. Number and Quantity
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):
4.NBT.B. Number & Operations in Base Ten: Use place value understanding and properties of operations to perform multi-digit arithmetic.
Fluently add and subtract multi-digit whole numbers using the standard algorithm. (CCSS: 4.NBT.B.4)
Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.* (CCSS: 4.NBT.B.5)
Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.** (CCSS: 4.NBT.B.6)
Solve multi-digit arithmetic problems. (Entrepreneurial Skills: Critical Thinking/Problem Solving)
Explain the process and result of multi-digit arithmetic. (MP3)
Precisely and efficiently add and subtract multi-digit numbers. (MP6)
Use the structure of place value to support the organization of mental and written multi-digit arithmetic strategies. (MP7)
Inquiry Questions
How can a visual model be used to demonstrate the relationship between multiplication and division?
Coherence Connections
This expectation represents major work of the grade.
In Grade 3, students use place value understanding and properties of operations to add and subtract within 1000 and to multiply and divide within 100.
In Grade 4, this expectation connects to using the four operations with whole numbers to solve problems.
In Grade 5, students understand the place value of decimals and perform operations with multi-digit whole numbers and with decimals to hundredths.
Academic Vocabulary & Language Expectations:
Commutative Property of Addition, Associative Property of Addition, Identity Property of Addition, count up, count down, compensation, variable, algorithm, inverse operations, Associative Property of Multiplication, partial products, numerical expression, Distributive Property, compensation, Commutative Property of Multiplication, remainder, partial quotients
Assessments:
Topic 2 Assessment (PDF), Topic 3 Assessment (PDF), Topic 4 Assessment (PDF), Topic 5 Assessment (PDF)
Instructional Resources & Notes:
enVision Mathematics Topics 2-5
Additional enVision Mathematics Resources
Let's Investigate! Read-a-Thon (TE) (supports Lessons 2-3, 2-4)
Let's Investigate! Tile the Floor (TE) (supports Lessons 3-3, 3-4)
Let's Investigate! Tile the Wall (TE) (supports Lessons 4-4, 4-5)
Let's Investigate! Packing Patterns (TE) (supports Lessons 5-2, 5-3, 5-4)
3-Act Math Recording Sheets (Topic 3, Topic 5)
Supplemental Lesson Resources: Topic 2, Topic 3, Topic 4, Topic 5
Additional Math Games: Multi-Digit Addition & Subtraction (additional materials and preparation may be required)
Additional Math Games: Multi-Digit Multiplication & Division (additional materials and preparation may be required)
Notes:
*Focus on conceptual strategies for multiplication in Topics 3-4, specifically using an area model and the distributive property to multiply. Students do not need to know or use the standard algorithm. (Students do not need to know or use the standard algorithm multiplying whole numbers until 5th Grade.)
**Focus on conceptual strategies for division in Topic 5, specifically using an area model or “partial quotients” to divide. Students do not need to know or use the standard algorithm.
It is recommended to reorder the lessons in Topic 5 as follows: Lesson 5-1, 5-2, 5-3, Let's Investigate!, 5-7, 3-Act Math, 5-8, 5-5, 5-6, 5-4, 5-9
Topic 3 Readiness Resources:
Prior to Topic 3, spend up to five days reviewing multiplication within 100, serving as an opportunity to review assumed prior knowledge from 3rd Grade before starting multi-digit multiplication in Topics 3 and 4. Activities and tasks may include:
Multiplication Fluency Games (from 3rd Grade) (reinforcing multiplication and division within 100 from 3rd Grade)
Youcubed.org Tasks (choose as appropriate): Tic-Tac-Toe Products, Math Cards, How Close to 100?, Circles & Stars, How Many Rows? How Many in Each Row?
Illustrative Mathematics Tasks (choose as appropriate): Kiri's Multiplication Matching Game, Valid Equalities (Part 2)
Math Diagnosis and Intervention System, Booklet G: Operations with Whole Numbers in Grades 4-6 (choose as appropriate): Lessons G21, G24, G25, G26, G27, G28, G29, G30, G31, G35
Tier 1 Intervention & Supports (i-Ready Tools for Instruction):
Tier 1 Intervention Topic 2: Add Multi-Digit Numbers, Subtract Multi-Digit Numbers
Tier 1 Intervention Topic 3: Multiply by One-Digit Numbers
Tier 1 Intervention Topic 4: Multiply by Two-Digit Numbers
Tier 1 Intervention Topic 5: Divide Three-Digit by One-Digit Numbers, Divide Four-Digit by One-Digit Numbers
Coherence Map/Concept Progressions: 4.NBT.B.4, 4.NBT.B.5, 4.NBT.B.6