Explore · measuring problem
7 kg of clay is divided into packets that each weigh 2/3 kg. How many packet-sized measures does that make? Count any partial packet as a fraction of a packet.
Great Inheritance Mathematics Term A · Independent learning
Word Problems
Learning target: Distinguish fraction-as-a-share from number-of-groups division in context.
Begin with the exact prerequisite checkpoint below. Afterward, explain why your strategy works, not merely which procedure to use.
Opening task
Lesson-specific prerequisite checkpoint
Do this without a worked example. If you cannot explain it, review the earlier skill before continuing.
What is the difference between sharing 12 in three groups and making groups of three?
Understand the idea
Distinguish fraction-as-a-share from number-of-groups division in context.
Division has two useful interpretations: sharing a known quantity among a number of people, and measuring how many groups of a known size fit inside a quantity. The language determines what the quotient means and what unit it carries.
Vocabulary focus: sharing interpretation, measurement interpretation, inverse multiplication. Make a small labeled model, work through the arithmetic, and explain the result in words.
Watch for: Using the wrong meaning of the quotient.
Model to study: Sharing versus measuring comparison.
Worked examples
Worked examples 1 · sharing problem
3/5 kg of clay is shared among 6 students equally. How many kg does each student receive?
Solution: 1/10 kg
Why: This is sharing: 3/5 ÷ 6 = 1/10 kg per student. Check 6 equal shares total 3/5 kg.
Worked examples 2 · measuring problem
5 kg of clay is divided into packets that each weigh 1/5 kg. How many packet-sized measures does that make? Count any partial packet as a fraction of a packet.
Solution: 25 packets
Why: This is number-of-groups division: 5 ÷ 1/5 = 25 packets; 25×1/5 kg = 5 kg.
Worked examples 3 · sharing problem
1/4 kg of clay is shared among 6 students equally. How many kg does each student receive?
Solution: 1/24 kg
Why: This is sharing: 1/4 ÷ 6 = 1/24 kg per student. Check 6 equal shares total 1/4 kg.
Check understanding
Check understanding 1 · measuring problem
5 kg of clay is divided into packets that each weigh 3/4 kg. How many packet-sized measures does that make? Count any partial packet as a fraction of a packet.
Check understanding 2 · sharing problem
2/3 kg of clay is shared among 2 students equally. How many kg does each student receive?
Guided practice
Guided practice 1 · measuring problem
7 kg of clay is divided into packets that each weigh 1/3 kg. How many packet-sized measures does that make? Count any partial packet as a fraction of a packet.
Guided practice 2 · sharing problem
1/5 kg of clay is shared among 4 students equally. How many kg does each student receive?
Guided practice 3 · sharing problem
1/3 kg of clay is shared among 2 students equally. How many kg does each student receive?
Independent practice
Independent practice 1 · sharing problem
4/5 kg of clay is shared among 4 students equally. How many kg does each student receive?
Independent practice 2 · measuring problem
6 kg of clay is divided into packets that each weigh 1/5 kg. How many packet-sized measures does that make? Count any partial packet as a fraction of a packet.
Independent practice 3 · sharing problem
2/5 kg of clay is shared among 5 students equally. How many kg does each student receive?
Independent practice 4 · measuring problem
4 kg of clay is divided into packets that each weigh 1/3 kg. How many packet-sized measures does that make? Count any partial packet as a fraction of a packet.
Independent practice 5 · sharing problem
1/4 kg of clay is shared among 3 students equally. How many kg does each student receive?
Challenge and error analysis
Challenge and error analysis 1 · worked-error diagnosis
Error-analysis notebook: Learner notebook (LESSON): “6 ÷ 4/5 = 24/5; I multiplied instead of counting how many 4/5-size groups fit.” Identify exactly which written step or assumption fails, correct it, and independently solve this new task: 6 kg of clay is divided into packets that each weigh 4/5 kg. How many packet-sized measures does that make? Count any partial packet as a fraction of a packet.
Challenge and error analysis 2 · reasoning transfer
Reasoning and transfer: Solve, then explain a different way to check your answer (inverse operation, estimate, model, or units as appropriate). 2/3 kg of clay is shared among 6 students equally. How many kg does each student receive?
Exit check
Exit check 1 · measuring problem
2 kg of clay is divided into packets that each weigh 3/5 kg. How many packet-sized measures does that make? Count any partial packet as a fraction of a packet.
Exit check 2 · sharing problem
3/4 kg of clay is shared among 3 students equally. How many kg does each student receive?
Target for independent mastery: all exit-check problems correct plus a justified explanation. A instructor may reteach the concept if calculations are correct without meaningful reasoning.