Longview ISD4th Grade Math Unit 3
4th Grade TEKS with Specificities4.4Number, operation, and quantitative reasoning. The student multiplies and divides to solve meaningful problems involving whole numbers. The student is expected to:
4.4Amodel factors and products using arrays and area models
Include:
- Using vocabulary such as factors, products, dimensions, and area
- Concrete to pictorial to abstract instruction must be made with area models or arrays.
- Arrays, unifix cubes, tiles, base 10 pieces, cm grid paper, linear pieces
Include:
- Create number sentences and relate to the fact families
- Apply multiplication/division concepts
- Journaling should explain the process
- Build from the concrete to the pictorial to the abstract number
- Factors, multiples, quotient, product
- Tiles, linear pieces, base 10 pieces
Include:
- Learn and apply multiplication facts (fact families), and extend fact families to include related factors (ex. 6 x 2 = 12 and 2 x 6 = 12 relate to 3x4 = 12 and 4 x 3 = 12)
- Factors, multiples, products
- Arrays, tiles, base 10 pieces
Include:
- Apply multiplication/division concepts
- Process through the representations: concrete/pictorial/abstract
- Concrete manipulatives for understanding concept of multiplication, base 10 pieces, grid paper
Include:
- Students build concrete models w/ and w/out remainders
- Students draw a representation of the model
- Students move to the abstract numbers from the concrete models and pictorial drawings
- divisor, dividend, remainder, quotient
- Concrete manipulatives for understanding concept of division, tiles, base 10 pieces
4.5Buse strategies including rounding and compatible numbers to estimate solutions to multiplication and division problems
Include:
- Round numbers before computation
- Use compatible numbers
- Work with examples of real-life estimation
- Use the situation in the problem to determine the rounding strategy. Such as: front end estimation (75 x 46 would be 70 x 40)
- for addition of two numbers and subtraction round to the highest place value of the smallest number used in computation (237-46 would be 24050)
- In multiplication and division round to the most reasonable place value of each number (for example, 58 x 63 would become 60 x 60)
- Compatible numbers (new skill) are “numbers that are easy to compute mentally.” For example:
- 25 + 46 + 75...think (25 + 75) + 46; which would be 100 + 46
- 78 + 96 can be computed as 75 + 100 or 78 + 100
- 4,126 ÷ 8 - think 4,000 ÷ 8 = 500
- Concrete manipulatives for understanding, base 10 pieces
4.6Ause patterns and relationships to develop strategies to remember basic multiplication and division facts (such as the patterns in related multiplication and division sentences (fact families) such as 9x9=81 and 81÷9=9
Include:
- Equations
- Real-life application
- Journal fact families - students include explanations on fact families
- Relate all factors to the product
- * Snap cubes, tiles, base ten pieces
Include:
- Find patterns using multiple representations.
- Tables
- Bar graphs
- Concrete/pictorial/abstract
- Real-life application
- Word problems
- "T" charts
- Tiles, base ten pieces, grid paper
4.7ADescribe the relationship between two sets of related data such as ordered pairs in a table
Include:
- Pictorial models
- Journal writing describing patterns
- Concrete/pictorial/abstract
- Real-life application
- Sets of objects, arrays, tiles, T charts, base ten pieces
Patterns and Problem Solving with Multiplication and Division
Vocabulary Adventure
- Dozen p. 25
- Product p.37
- Factor p. 39
- Array p. 41
- Quotient p. 43
- Divisor p. 45
- Dividend p. 47
- Remainder p. 49
- Fact family p. 57
- Inverse operation p. 59
- Pattern p. 63
Arrays and Shares
- Investigation 1 “Multiples on the 100 Chart” Sessions 1-3
- Investigation 2 “Arrays” Sessions 5-8
- Investigation 3 “Multiplication Clusters”Sessions 1-2 (Read p. 47 Teacher Note prior to lesson and use only if students are ready).
- Investigation 2 Session 1 “Factors of 100, 200, and 300”
- Investigation 3 Sessions 1-2—revisit the 1000 book from Unit 1
- Investigation 3 Sessions 1-2 “Division Notation and Situations”
- Session 3 “Look More Closely at Division Problems”
- Sessions 7-8 “What are Numbers Divisible By?”
- Session 9 “Division Bingo” (see Teacher Notes on pp. 39 and 45)
(These lessons teach the same concepts as Investigations; teacher preference to format will decide which to use.)
Teacher Reference ManualChapter 6“Numeration: Multiplication and Division (pp. 47-61)
Volume 1—Contact Lessons 5-9 (pp. 6-15)
Volume 2—Insight Lessons 76, 78-86, and 92-100 (pp. 102-153)
TEXTEAMS
Number Concepts section
- “Do I Get a Prize?” multiples, factors, patterns, squares
- “Finding Factors” multiply by 2-digit numbers to estimate
- “Multiplication Table Patterns”
- “Belongs, Doesn’t Belong” use patterns to discover rules to sort a set of numbers
- “Plaids” patterns on multiplication table to develop proficiency with basic facts
- “Two’s are Too Much” explore divisibility rules
Chapter 4 Multiplication and Division of Whole Numbers Lessons 18-25
Chapter 5 Patterns and Relationships Lessons 27-29
Math Essentials
- Multiplication starts p. 33
- Division starts p. 41
- Problem Solving with Multiplication and Division starts p. 49
- Estimating and rounding with mult/div are mixed within those 2 sections starting on p. 53
- Patterns, tables, number pairs p. 61-
“Make a Table”
- Count On It p. 58
- Problem Solver II Teaching Problem #3, p.6 and #4, p. 8
- Measuring Up p. 220
- Count OnIt p.66
- Problem Solver II Teaching Problem #1, p.2
- Measuring Up p. 91
- Count On It p. 42-43
- Problem Solver II Teaching Problem #9, p. 18 and #10, p. 20
- Measuring Up pp. 18-19
8/27/2007DRAFT 3