Exploring Multiplication and Division: Practical Applications and Teaching Strategies

Practical Questions

Propose flexible methods for learning operations based on the properties of numbers and compare them with standard algorithms. Analyze children's productions and strategies. Propose/analyze "racons" to work on division, justifying them from mathematical, educational, and curricular perspectives.

Division Corner

Through the drawing of flower petals, we'll distribute them in equal parts without any remainders. Last question: How many petals does each flower have? Is that the only possible solution? (Materials: worksheet with flowers printed or paper to draw, paper cut-outs of the petals)

Solving

24 petals = 6 flowers of 4. They do one, then the next, and then the next = commutative property.

Parts of Each Activity

• Name
• Description
• SC
• Structures
• Metaphors
• Properties
• Representations
• Re/productive practice

Propose/Analyze

Productive Practice

• On algorithms: Justifying them from mathematical, educational, and curricular perspectives.
• On geometry: Justifying them from mathematical, educational, and curricular perspectives.
• Related to "carnestoltes": Justifying them from mathematical, educational, and curricular perspectives.
• Connect arithmetic and geometry: Justifying them from mathematical, educational, and curricular perspectives.
• Shapes/position/visualization: Justify how to use them from mathematical, educational, and curricular perspectives.

Multiplication: Visual Models

• Repeated addition of isolated units: 4 packets of 5 cards: 20.
• Repeated addition of length: Add 6 towers of 4 Lego pieces: tower of 24.
• Repeated movements along the line: Jumps 5 units every time, in 3 times: 15 meters.
• Area of a rectangle/Distribution: 7 rows of 10 stars.
• Combination: First step is to work on easy strategies such as 2x5: 10 and then decompose numbers to obtain simpler ones 8x7: 8x(5+2).

Properties

• Associative: Decompose numbers - (7=5+2=4+3)
• Distributive: Split the multiplication - (8x(5+2) = 8x5 + 8x2)
• Commutative: Change the order of the factor to make it easier (8x3 = 3x8).

How to Teach

1. One: Basic multiplications in tables through repetition.
2. Two: Patterns, two is always even, repetition but helps memorization.
3. Three: Tables are made by the students, using strategies (calculate doubles/halves) focusing on deduction and the main properties of numbers and the numeral system.

Division

• Partition: How many groups do we have? Or how many times have we done the repetition?
• Sharing: How many units does each group have? Or what is the magnitude that has been repeated?