35:55
4th Grade Math
Massachusetts DESE
Overview
This video introduces the concept of multiplicative comparisons in 4th-grade math. It begins with a 'quick images' activity to activate prior knowledge about visualizing and representing numbers through arrays and multiplication. The core of the lesson focuses on understanding and applying multiplicative comparisons through a think-pair-share activity and a detailed word problem about apples. The lesson emphasizes identifying the relationship where one quantity is a multiple of another, using visual aids and mathematical equations to solidify understanding. It concludes by reinforcing the definition and application of multiplicative comparisons, preparing students for further practice.
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Chapters
- Quick images activity involves briefly viewing a visual and then drawing or describing it from memory.
- This activity helps students visualize quantities and connect them to mathematical equations.
- Students can interpret the same visual in different ways, leading to discussions about the commutative property (e.g., 3x6 vs. 6x3).
- The visual representation can be understood as an array, which is a structured arrangement of items in rows and columns.
This warm-up activates visual memory and connects abstract numbers to concrete representations like arrays, reinforcing foundational multiplication concepts before introducing new vocabulary.
Students see a visual, then draw it and create equations like 3x6=18 or 9x2=18, discussing how they saw the arrangement (e.g., groups of six or groups of two).
- Multiplicative comparison involves understanding relationships where one quantity is a multiple of another.
- Students are encouraged to use their reading comprehension skills (schema, root words) to decipher the meaning of mathematical terms.
- Initial student ideas for 'multiplicative comparison' include comparing multiplication problems or finding multiples.
- The key idea is to compare quantities using multiplication, often involving phrases like 'times as many' or 'times as tall'.
This section introduces a new mathematical term and encourages students to actively construct its meaning, fostering deeper understanding and metacognitive skills.
Students brainstorm the meaning of 'multiplicative comparison,' connecting 'multiplicative' to multiplication and 'comparison' to comparing quantities.
- The problem involves two characters, Tiandra and Reese, and their apples.
- Tiandra picked 7 apples, and Reese picked 'four times as many' apples.
- The task is to find the total number of apples Reese picked.
- Visualizing the problem involves creating groups of 7 apples, repeated four times, to represent 'four times as many'.
- The solution is found by calculating 4 x 7 = 28 apples, emphasizing the label 'apples' in the answer.
This concrete example allows students to apply the concept of multiplicative comparison to solve a real-world scenario, solidifying the relationship between the quantities.
Visualizing Tiandra's 7 yellow apples and then drawing Reese's apples as four groups of 7, leading to the calculation 4 x 7 = 28 apples.
- Students analyze a second problem (sister's height) and compare it to the apple problem, looking for repeated phrases like 'times as many' or 'times as tall'.
- The core concept is comparing the factors within a multiplication equation in the context of a story problem.
- Multiplicative comparison is not about comparing two different multiplication problems (e.g., 7x4 vs. 2x3), but about the relationship between quantities described multiplicatively.
- The phrase '28 is four times as many as 7' is a key way to express a multiplicative comparison, highlighting the relationship between the product and one of the factors.
This chapter refines the definition by contrasting correct and incorrect interpretations, helping students grasp the specific meaning of multiplicative comparison and its structure.
Comparing the apple problem (Reese picked 4 times as many apples as Tiandra) and the height problem (Dad is 3 times as tall as his sister) to identify the common structure and meaning.
- Multiplication facts can be expressed in various ways, including arrays (e.g., 'four rows of seven') and phrases.
- A key way to express multiplicative comparison is 'Product is X times as many as Factor'.
- Students learn to correctly phrase the relationship, such as '28 is four times as many as 7', not '7 is 28 times as many as 4'.
- Understanding this phrasing requires correctly identifying the factors and the product in a multiplication scenario.
Learning to articulate multiplicative comparisons in precise language helps students internalize the concept and use it accurately in future problem-solving.
Learning to say 'Twenty-eight is four times as many as seven' and understanding why 'Seven is twenty-eight times as many as four' is incorrect based on the numbers involved.
Key takeaways
- Visualizing math problems, like in quick images, helps connect abstract concepts to concrete representations.
- Understanding mathematical vocabulary involves using prior knowledge and breaking down terms.
- Multiplicative comparison describes a relationship where one quantity is a whole number multiple of another.
- Word problems involving 'times as many' or 'times as tall' are examples of multiplicative comparisons.
- The structure 'Product is X times as many as Factor' is a key way to express multiplicative comparisons.
- Accurate labeling of answers in word problems is crucial for clarity.
- The commutative property allows for different ways to view arrays and multiplication facts, but multiplicative comparison focuses on a specific type of relationship.
Key terms
Quick ImagesArrayCommutative PropertyMultiplicative ComparisonsFactorsProductTimes as manyTimes as tallSchema
Test your understanding
- How does the 'quick images' activity help students prepare for learning about multiplicative comparisons?
- What is the difference between comparing two multiplication problems and a multiplicative comparison?
- Explain how to solve the apple problem using the concept of multiplicative comparison.
- What does the phrase 'X is Y times as many as Z' mean in mathematics?
- How can understanding root words and prefixes help in learning new math vocabulary like 'multiplicative comparison'?