Lesson 21
Independent Task
Lesson 22
Math Quiz
Our pre-class checklist:
Are you sitting at a desk in a well lit room?
Are you in a quiet room?
Do you have your bina materials?
Are you saving food for after class?
Did you arrive a few minutes early?
Are we ready and focused?
Lesson 18
Maths: POSITIVE INTEGER SCALING
Lesson goals
- I can solve positive integer scaling problems and correspondence problems
Materials: - Writing surface (Paper or whiteboard preferred)
- Greylead pencil or pen
- Colouring tools (crayons/markers/colour pencils)
WARM-UP: COMPARISON LANGUAGE
Count together:
Which shows more?
• 5 apples vs 15 apples
• How many times as many? (3 times)
LAUNCH: UNDERSTANDING SCALING
San people tracking animals
A San tracker sees 7 springbok in the morning. In the afternoon, she sees 3 times as many springbok. How many springbok in the afternoon?
Problem: 3 times as many as 7
STEP 2
STEP 3
STEP 4
STEP 1
Understand "times as many"
• "Times as many" means multiply
• 3 times as many as 7 = 3 × 7
Visualize with bar model
• Morning: [7 springbok]
• Afternoon: [7][7][7] ← three groups of 7
• Afternoon = 3 × 7
Calculate
• 3 × 7 = 21 springbok
Check understanding
• Is 21 three times as many as 7?
• 21 ÷ 7 = 3 ✓
Answer: 21 springbok in the afternoon.
More examples
Finding the Original Amount
A ranger walked 4 times as many kilometers as another ranger. The first ranger walked 28 km. How many did the second ranger walk?
• 4 × ? = 28
• 28 ÷ 4 = 7 km
Finding the Scale Factor
One camp has 6 tents. Another camp has 42 tents. How many times as many tents does the second camp have?
• ? times as many as 6 = 42
• ? × 6 = 42
• 42 ÷ 6 = 7
• 7 times as many
Direct Scaling
A garden has 8 trees. Another garden has 4 times as many trees. How many in the second garden?
• 4 times as many as 8 = 4 × 8 = 32 trees
Use this side of the card to provide more information about a topic. Focus on one concept. Make learning and communication more efficient.
Use this side of the card to provide more information about a topic. Focus on one concept. Make learning and communication more efficient.
Use this side of the card to provide more information about a topic. Focus on one concept. Make learning and communication more efficient.
Example 1
Example 2
Example 3
Title
Title
Title
Write a brief description here
Write a brief description here
Write a brief description here
EXPLORE: SCALING PRACTICE
Activity 1: Times as Many Problems
Set C
Set B
Set A
Discussion Questions:
• How are multiplication and division related?
• How does knowing times tables help with division?
• When is estimation useful?
Practicing Humanity:
When I got stuck, I tried a different strategy: ___.
Our pre-class checklist:
Are you sitting at a desk in a well lit room?
Are you in a quiet room?
Do you have your bina materials?
Are you saving food for after class?
Did you arrive a few minutes early?
Are we ready and focused?
Lesson 19
Maths: CORRESPONDENCE PROBLEMS
Lesson goals
- I can solve positive integer scaling problems and correspondence problems.
WARM-UP: SPOTTING PATTERNS
What pattern do you see?
1 basket → 7 items
2 baskets → 14 items
3 baskets → 21 items
Launch: UNDERSTANDING CORRESPONDENCE
San people organizing supplies
Each San family needs 8 water containers for a journey. How many containers for different numbers of families?
Pattern/Relationship: 1 family → 8 containers
2 families → 16 containers
3 families → 24 containers
4 families → 32 containers
Find total (given groups)
If 6 families travel, how many containers needed?
• 6 families × 8 containers each = 48 containers
Problem Type 1
Find groups (given total)
If there are 56 containers, how many families?
• 56 containers ÷ 8 per family = 7 families
Problem Type 2
Find rate (given groups and total)
9 families need 63 containers. How many per family?
• 63 containers ÷ 9 families = 7 per family
Problem Type 3
Creating a table
Families
Containers
1 2 3 4 5
8 16 24 32 40
Pattern: Multiply families by 8 to get containers
EXPLORE: CORRESPONDENCE PRACTICE
Activity 1: Rate Problems
Calculation Space
Tree Planting
Each conservation team plants 7 trees per day.
a) How many trees do 4 teams plant in one day?
b) If 63 trees were planted, how many teams?
c) Create a table showing 1-5 teams
Problem 2
Calculation Space
Water Collection
Each collection point gathers 9 liters per hour.
a) How many liters from 6 points in one hour?
b) If 72 liters collected in one hour, how many points?
c) How many liters from 8 points?
Problem 3
Calculation Space
Animal Tracking
A tracker sees 4 springbok tracks per 100 meters.
a) How many tracks in 300 meters?
b) If she counted 28 tracks, how many hundreds of meters?
c) How many tracks in 900 meters?
Activity 2: Real Kalahari Scenarios
Problem 4:
Rangers give each visitor 3 information cards. They gave out 48 cards. How many visitors?
Problem 5:
Each ranger station needs 8 solar panels. There are 7 stations. How many panels total?
Problem 6:
A garden has 9 plants per row. There are 6 rows. How many plants total? If they add 3 more rows, what's the new total?
Calculation Space
Problem 7:
Create your own correspondence problem:
Tasks:
• Make tables when helpful
• Show multiplication/division
• Write answers with units
• Check patterns make sense
• Choose a rate (items per group)
• Make up a question
• Solve it!
Discussion Questions:
• What makes something a correspondence problem?
• How do tables help?
• When do you multiply? Divide?
Practicing Humanity:
I checked my progress and noticed I improved at…
Our pre-class checklist:
Are you sitting at a desk in a well lit room?
Are you in a quiet room?
Do you have your bina materials?
Are you saving food for after class?
Did you arrive a few minutes early?
Are we ready and focused?
Lesson 20
Maths: SCALING AND CORRESPONDENCE
Lesson goals
- I can revise multiplication/division missing numbers, scaling, correspondence
WARM-UP: SKILLS REVIEW
• 7 × ? = 63 (missing factor)
• A camp has 6 tents. Another has 4 times as many. How many? (scaling)
• Each ranger needs 8 items. 5 rangers need how many items? (correspondence)
LAUNCH: ADVENTURE OVERVIEW
The Challenge: Kalahari Conservation Project Planning San communities are working with conservation teams to plan a major initiative. Multiple problems must be solved using Week 4 skills!
Step-by-Step Solution:
a) Scaling: 7 times as many as 9 = 7 × 9 = 63 collection points
b) Correspondence: 63 points × 8 liters each = 504 liters per day
Sample Problem - Water Resource Planning:
Community A has 9 water collection points. Community B has 7 times as many collection points. Each collection point in Community B gathers 8 liters per day.
a) How many collection points in Community B?
b) How many liters does Community B collect per day?
EXPLORE: ADVENTURE MISSIONS
Complete All Missions - Partner or Small Group Work:
Mission 3
Mission 2
Mission 1
Complete All Missions - Partner or Small Group Work:
Mission 6
Mission 5
Mission 4
SUMMARISE: MISSION DEBRIEF
• Which mission was most challenging?
• What Week 4 skills did you use most?
• How did you know which operation to use?
• What strategies helped when stuck?
Our pre-class checklist:
Are you sitting at a desk in a well lit room?
Are you in a quiet room?
Do you have your bina materials?
Are you saving food for after class?
Did you arrive a few minutes early?
Are we ready and focused?
Lesson 21
Maths: REVISION
Lesson goals
- I can revise all topics from the biome
Revision: mixed practice
Lesson 21
Independent Task
Our pre-class checklist:
Are you sitting at a desk in a well lit room?
Are you in a quiet room?
Do you have your bina materials?
Are you saving food for after class?
Did you arrive a few minutes early?
Are we ready and focused?
Lesson 22
Maths: Asessement
Lesson goals
- I can complete a quiz (assessment) of our learning
End of biome quiz
Lesson 22
Math Quiz
Garden Expansion
A botanical garden expands:
• Original garden has 7 plant sections
• Each section has some number of plants
• Original garden has 56 plants total
• Expansion will be 3 times as large as original
a) How many plants per section in original?
b) How many plants in expanded garden?
c) If expanded garden adds 4 more sections (same plants per section), what's new total?
Tree Nursery Operations
A tree nursery organizes seedlings:
• Small nursery has 8 types of trees
• Large nursery has 9 times as many types
• Each type has some number of seedlings
• Large nursery has 648 seedlings total
a) How many tree types in large nursery?
b) How many seedlings per type in large nursery?
Key Concepts: • "Times as many" means multiplication • Three types of scaling problems:
1. Find scaled amount (multiply)
2. Find scale factor (divide)
3. Find original amount (divide)
• Bar models show comparison visually
• Check: does answer make sense?
Key Concepts: • "Times as many" means multiplication • Three types of scaling problems:
1. Find scaled amount (multiply)
2. Find scale factor (divide)
3. Find original amount (divide)
• Bar models show comparison visually
• Check: does answer make sense?
Water Distribution Network
A water distribution system:
• Distribution Point 1 serves 6 families
• Distribution Point 2 serves 4 times as many families
• Each family needs 9 liters per day
a) How many families at Point 2?
b) How many liters needed at Point 2 per day?
c) What's the total for both points combined?
Ranger Station Supplies
Ranger stations need supplies:
• Each station needs 7 supply kits
• Some number of stations need supplies
• 63 supply kits total needed
• Each kit contains 9 items
a) How many ranger stations?
b) How many items total across all kits?
Find the Original Amount:
g) A tracker walked 6 times as far as another. The first walked 54 km. How far did the second walk?
h) One group collected 7 times as much water as another. The first group collected 49 liters. How much did the second group collect?
Find the Scaled Amount:
a) A water hole has 9 liters. Another has 7 times as many liters. How many in the second?
b) One area has 6 meerkats. Another area has 8 times as many. How many meerkats?
c) A small garden has 4 plant types. A large garden has 9 times as many types. How many types?
Animal Population Study
San trackers study meerkat colonies:
• Colony A has some number of meerkats
• Colony B has 8 times as many meerkats as Colony A
• Colony B has 72 meerkats
• Trackers observe that each meerkat digs 4 burrows
a) How many meerkats in Colony A?
b) How many burrows total in Colony B?
Find the Scale Factor:
d) Camp A has 5 rangers. Camp B has 35 rangers. How many times as many rangers in Camp B?
e) One tree is 8 meters tall. Another is 72 meters tall. How many times as tall?
f) A container has 7 liters. Another has 63 liters. How many times as much?
Solar Panel Installation
Conservation camp installs solar panels:
• Small camp has 4 panels
• Medium camp has 7 times as many as small camp
• Large camp has ? panels (unknown)
• All camps together have 88 panels
a) How many panels at medium camp?
b) How many panels at large camp?
Key Concepts: • "Times as many" means multiplication • Three types of scaling problems:
1. Find scaled amount (multiply)
2. Find scale factor (divide)
3. Find original amount (divide)
• Bar models show comparison visually
• Check: does answer make sense?
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Transcript
Lesson 21
Independent Task
Lesson 22
Math Quiz
Our pre-class checklist:
Are you sitting at a desk in a well lit room?
Are you in a quiet room?
Do you have your bina materials?
Are you saving food for after class?
Did you arrive a few minutes early?
Are we ready and focused?
Lesson 18
Maths: POSITIVE INTEGER SCALING
Lesson goals
Materials:- Writing surface (Paper or whiteboard preferred)
- Greylead pencil or pen
- Colouring tools (crayons/markers/colour pencils)
WARM-UP: COMPARISON LANGUAGE
Count together:
Which shows more? • 5 apples vs 15 apples • How many times as many? (3 times)
LAUNCH: UNDERSTANDING SCALING
San people tracking animals A San tracker sees 7 springbok in the morning. In the afternoon, she sees 3 times as many springbok. How many springbok in the afternoon? Problem: 3 times as many as 7
STEP 2
STEP 3
STEP 4
STEP 1
Understand "times as many" • "Times as many" means multiply • 3 times as many as 7 = 3 × 7
Visualize with bar model • Morning: [7 springbok] • Afternoon: [7][7][7] ← three groups of 7 • Afternoon = 3 × 7
Calculate • 3 × 7 = 21 springbok
Check understanding • Is 21 three times as many as 7? • 21 ÷ 7 = 3 ✓ Answer: 21 springbok in the afternoon.
More examples
Finding the Original Amount A ranger walked 4 times as many kilometers as another ranger. The first ranger walked 28 km. How many did the second ranger walk? • 4 × ? = 28 • 28 ÷ 4 = 7 km
Finding the Scale Factor One camp has 6 tents. Another camp has 42 tents. How many times as many tents does the second camp have? • ? times as many as 6 = 42 • ? × 6 = 42 • 42 ÷ 6 = 7 • 7 times as many
Direct Scaling A garden has 8 trees. Another garden has 4 times as many trees. How many in the second garden? • 4 times as many as 8 = 4 × 8 = 32 trees
Use this side of the card to provide more information about a topic. Focus on one concept. Make learning and communication more efficient.
Use this side of the card to provide more information about a topic. Focus on one concept. Make learning and communication more efficient.
Use this side of the card to provide more information about a topic. Focus on one concept. Make learning and communication more efficient.
Example 1
Example 2
Example 3
Title
Title
Title
Write a brief description here
Write a brief description here
Write a brief description here
EXPLORE: SCALING PRACTICE
Activity 1: Times as Many Problems
Set C
Set B
Set A
Discussion Questions:
• How are multiplication and division related? • How does knowing times tables help with division? • When is estimation useful?
Practicing Humanity: When I got stuck, I tried a different strategy: ___.
Our pre-class checklist:
Are you sitting at a desk in a well lit room?
Are you in a quiet room?
Do you have your bina materials?
Are you saving food for after class?
Did you arrive a few minutes early?
Are we ready and focused?
Lesson 19
Maths: CORRESPONDENCE PROBLEMS
Lesson goals
WARM-UP: SPOTTING PATTERNS
What pattern do you see? 1 basket → 7 items 2 baskets → 14 items 3 baskets → 21 items
Launch: UNDERSTANDING CORRESPONDENCE
San people organizing supplies Each San family needs 8 water containers for a journey. How many containers for different numbers of families?
Pattern/Relationship: 1 family → 8 containers 2 families → 16 containers 3 families → 24 containers 4 families → 32 containers
Find total (given groups) If 6 families travel, how many containers needed? • 6 families × 8 containers each = 48 containers
Problem Type 1
Find groups (given total) If there are 56 containers, how many families? • 56 containers ÷ 8 per family = 7 families
Problem Type 2
Find rate (given groups and total) 9 families need 63 containers. How many per family? • 63 containers ÷ 9 families = 7 per family
Problem Type 3
Creating a table
Families
Containers
1 2 3 4 5
8 16 24 32 40
Pattern: Multiply families by 8 to get containers
EXPLORE: CORRESPONDENCE PRACTICE
Activity 1: Rate Problems
Calculation Space
Tree Planting Each conservation team plants 7 trees per day. a) How many trees do 4 teams plant in one day? b) If 63 trees were planted, how many teams? c) Create a table showing 1-5 teams
Problem 2
Calculation Space
Water Collection Each collection point gathers 9 liters per hour. a) How many liters from 6 points in one hour? b) If 72 liters collected in one hour, how many points? c) How many liters from 8 points?
Problem 3
Calculation Space
Animal Tracking A tracker sees 4 springbok tracks per 100 meters. a) How many tracks in 300 meters? b) If she counted 28 tracks, how many hundreds of meters? c) How many tracks in 900 meters?
Activity 2: Real Kalahari Scenarios
Problem 4: Rangers give each visitor 3 information cards. They gave out 48 cards. How many visitors? Problem 5: Each ranger station needs 8 solar panels. There are 7 stations. How many panels total? Problem 6: A garden has 9 plants per row. There are 6 rows. How many plants total? If they add 3 more rows, what's the new total?
Calculation Space
Problem 7: Create your own correspondence problem:
Tasks: • Make tables when helpful • Show multiplication/division • Write answers with units • Check patterns make sense
• Choose a rate (items per group) • Make up a question • Solve it!
Discussion Questions:
• What makes something a correspondence problem? • How do tables help? • When do you multiply? Divide?
Practicing Humanity: I checked my progress and noticed I improved at…
Our pre-class checklist:
Are you sitting at a desk in a well lit room?
Are you in a quiet room?
Do you have your bina materials?
Are you saving food for after class?
Did you arrive a few minutes early?
Are we ready and focused?
Lesson 20
Maths: SCALING AND CORRESPONDENCE
Lesson goals
WARM-UP: SKILLS REVIEW
• 7 × ? = 63 (missing factor) • A camp has 6 tents. Another has 4 times as many. How many? (scaling) • Each ranger needs 8 items. 5 rangers need how many items? (correspondence)
LAUNCH: ADVENTURE OVERVIEW
The Challenge: Kalahari Conservation Project Planning San communities are working with conservation teams to plan a major initiative. Multiple problems must be solved using Week 4 skills!
Step-by-Step Solution: a) Scaling: 7 times as many as 9 = 7 × 9 = 63 collection points b) Correspondence: 63 points × 8 liters each = 504 liters per day
Sample Problem - Water Resource Planning: Community A has 9 water collection points. Community B has 7 times as many collection points. Each collection point in Community B gathers 8 liters per day. a) How many collection points in Community B? b) How many liters does Community B collect per day?
EXPLORE: ADVENTURE MISSIONS
Complete All Missions - Partner or Small Group Work:
Mission 3
Mission 2
Mission 1
Complete All Missions - Partner or Small Group Work:
Mission 6
Mission 5
Mission 4
SUMMARISE: MISSION DEBRIEF
• Which mission was most challenging? • What Week 4 skills did you use most? • How did you know which operation to use? • What strategies helped when stuck?
Our pre-class checklist:
Are you sitting at a desk in a well lit room?
Are you in a quiet room?
Do you have your bina materials?
Are you saving food for after class?
Did you arrive a few minutes early?
Are we ready and focused?
Lesson 21
Maths: REVISION
Lesson goals
Revision: mixed practice
Lesson 21
Independent Task
Our pre-class checklist:
Are you sitting at a desk in a well lit room?
Are you in a quiet room?
Do you have your bina materials?
Are you saving food for after class?
Did you arrive a few minutes early?
Are we ready and focused?
Lesson 22
Maths: Asessement
Lesson goals
End of biome quiz
Lesson 22
Math Quiz
Garden Expansion A botanical garden expands: • Original garden has 7 plant sections • Each section has some number of plants • Original garden has 56 plants total • Expansion will be 3 times as large as original a) How many plants per section in original? b) How many plants in expanded garden? c) If expanded garden adds 4 more sections (same plants per section), what's new total?
Tree Nursery Operations A tree nursery organizes seedlings: • Small nursery has 8 types of trees • Large nursery has 9 times as many types • Each type has some number of seedlings • Large nursery has 648 seedlings total a) How many tree types in large nursery? b) How many seedlings per type in large nursery?
Key Concepts: • "Times as many" means multiplication • Three types of scaling problems: 1. Find scaled amount (multiply) 2. Find scale factor (divide) 3. Find original amount (divide) • Bar models show comparison visually • Check: does answer make sense?
Key Concepts: • "Times as many" means multiplication • Three types of scaling problems: 1. Find scaled amount (multiply) 2. Find scale factor (divide) 3. Find original amount (divide) • Bar models show comparison visually • Check: does answer make sense?
Water Distribution Network A water distribution system: • Distribution Point 1 serves 6 families • Distribution Point 2 serves 4 times as many families • Each family needs 9 liters per day a) How many families at Point 2? b) How many liters needed at Point 2 per day? c) What's the total for both points combined?
Ranger Station Supplies Ranger stations need supplies: • Each station needs 7 supply kits • Some number of stations need supplies • 63 supply kits total needed • Each kit contains 9 items a) How many ranger stations? b) How many items total across all kits?
Find the Original Amount: g) A tracker walked 6 times as far as another. The first walked 54 km. How far did the second walk? h) One group collected 7 times as much water as another. The first group collected 49 liters. How much did the second group collect?
Find the Scaled Amount: a) A water hole has 9 liters. Another has 7 times as many liters. How many in the second? b) One area has 6 meerkats. Another area has 8 times as many. How many meerkats? c) A small garden has 4 plant types. A large garden has 9 times as many types. How many types?
Animal Population Study San trackers study meerkat colonies: • Colony A has some number of meerkats • Colony B has 8 times as many meerkats as Colony A • Colony B has 72 meerkats • Trackers observe that each meerkat digs 4 burrows a) How many meerkats in Colony A? b) How many burrows total in Colony B?
Find the Scale Factor: d) Camp A has 5 rangers. Camp B has 35 rangers. How many times as many rangers in Camp B? e) One tree is 8 meters tall. Another is 72 meters tall. How many times as tall? f) A container has 7 liters. Another has 63 liters. How many times as much?
Solar Panel Installation Conservation camp installs solar panels: • Small camp has 4 panels • Medium camp has 7 times as many as small camp • Large camp has ? panels (unknown) • All camps together have 88 panels a) How many panels at medium camp? b) How many panels at large camp?
Key Concepts: • "Times as many" means multiplication • Three types of scaling problems: 1. Find scaled amount (multiply) 2. Find scale factor (divide) 3. Find original amount (divide) • Bar models show comparison visually • Check: does answer make sense?