Solutions to pages 144, 145, and 146 of the "Student's Weapon" mathematics textbook for the fourt...

Solutions to pages 144, 145, and 146 of the fourth-grade math textbook, "Al-Tilmiz" (The Student's Weapon) Explanation of the associative property in multiplication for fourth grade Applying patterns in multiplication for fourth grade, first term Al-Tilmiz exercises on the associative property in multiplication Solutions to Al-Tilmiz exercises, fourth-grade math, Unit 5 Explanation of the second concept in multiplication for fourth-grade math Solved problems from the Al-Tilmiz textbook for fourth grade on the associative property Questions from educational administrations on the associative property for fourth-grade math Solutions to activities and exercises for Lessons 6 and 7, fourth-grade math Review of Unit 5, Al-Tilmiz math, fourth grade --- 🔖 Video Hashtags And the publications: #AlTilmiz_Weapon #Fourth_Grade_Elementary #Fourth_Grade_Math #Unit_Five #Associative_Property #Applying_Patterns #Solving_Exercises #Lesson_Explanation #Excellence_in_Mathematics #Online_School #Elementary_Math #Online_Learning #Your_Lesson_with_Mr_Mohamed #Math_Review #Educational_Channel ---To solve pages 144, 145, and 146 (Lessons 6 and 7) — Unit Five, Fourth Grade — Al-Tilmiz Weapon exercises, with solved step-by-step examples, and sample ministerial/administrative questions with solutions. Focused on: the associative property and applying patterns in multiplication (the second concept) — ready to print or explain in a video/Reels. The objective now is: 1. To understand the associative property of multiplication: how to change the order of division/association within multiplication without changing the result (a × (b × c) = (a × b) × c). 2. To use patterns (models such as: multiplying by 10, multiplying multiples, dividing by parts) to simplify calculations. 3. To solve practice questions and then questions from educational administrations (word problems and cumulative problems). --- 1) Quick explanation of Lesson 6 — The Associative Property of Multiplication Text: If we multiply three numbers together, we can change the way they are grouped without changing the result. Its formula: a × (b × c) = (a × b) × c Why do we use it? To simplify the calculation: we choose a grouping that produces numbers that are easy to multiply (example: grouping factors to make a multiple of 10 or 100). Solved Examples 1. Example 1: 2 × (3 × 5) Solution: 3 × 5 = 15 → 2 × 15 = 30. Alternatively: (2 × 3) × 5 = 6 × 5 = 30. The result is the same = 30. 2. Example 2: 4 × (5 × 25) Practical Solution: 5 × 25 = 125 → 4 × 125 = 500. Or (4 × 5) = 20 → 20 × 25 = 500. The result is 500. (We choose the grouping that gives the easier multiplication). 3. Example 3: 3 × (10 × 4) Here, 10 × 4 = 40 → 3 × 40 = 120. Or, (3 × 10) = 30 → 30 × 4 = 120. The result is 120. --- 2) Lesson 7 Explanation — Applying Patterns in Multiplication (Concept 2) Concept 2 of Multiplication: Viewing multiplication as repeated addition or as patterns/squares/rows (e.g., rows and columns in a matrix). Common patterns include: multiplying by 10 and 100; multiplying using multiples (2 ×, 5 ×, 25 ×); and using one-half/multipliers for ease of calculation (e.g., 6 × 15 = 3 × 30). Examples of Using Patterns 1. Multiplying by 10 or 100: 7 × 10 = 70 (add a zero). 36 × 100 = 3600 (add two zeros). 2. Substitution for simplification: 6 × 15 → because 15 = 3 × 5 → 6 × 15 = 6 × (3 × 5) = (6 × 3) × 5 = 18 × 5 = 90. Or 6 × 15 = 3 × 30 = 90 (use a halve/multiply). 3. Using grouping to make 10 or 100: 4 × 25 × 10 → (4 × 25) = 100 → 100 × 10 = 1000. (Here we chose grouping that gives 100). Solved Examples 1. Example 1: 8 × 125 Method: 125 = 25 × 5 → 8 × 125 = 8 × (25 × 5) = (8 × 25) × 5 = 200 × 5 = 1000. 2. Example 2: 12 × 25 Because 25 × 4 = 100 → We rearrange: 12 × 25 = (12 × 25) = (3 × 4) × 25 = 3 × (4 × 25) = 3 × 100 = 300. (Or directly: 12 × 25 = (12/4) × 100 = 3 × 100 = 300). 3. Example 3: 7 × 14 14 = 7 × 2 → 7 × 14 = 7 × (7 × 2) = (7 × 7) × 2 = 49 × 2 = 98. Or 14 × 7 is repeated addition. --- 3) General Steps for Solving Exercises on Pages 144–146 1. Read the problem completely and determine what is required (calculating a result, completing, simplifying). 2. If there are three factors, consider the associative property: Can the factors be combined to form 10, 100, 25, 50, etc.? 3. Use patterns: multiply by 10 → add a zero, multiply by 5 → halve, then multiply by 10, etc. 4. Re-evaluate: Calculate the result using the simplest step. Write each step clearly (important for exams). 5. Check the result by rounding or estimating it slightly (e.g., 8 × 125 ≈ 8 × 100 + 8 × 25 = 800 + 200 = 1000) to confirm. --- 4) Sample Questions from Educational Administrations — Expected Problems with Complete Solutions Question (A) — Simple Word Problem Question: Fatima arranged 3 rows of tables. Each row has 8 tables, and each table needs 4 books. How many books does Fatima need? Solution: Number of tables = 3 × 8 = 24 tables. Books = 24 × 4 = 96 books. (Or us...