Whole class
Ako 3
Maths planning
Term 3
Week: 10 | Curriculum Level: Lv 3 Area: Coordinates |
Teaching Focus: Model and support the use of questions which clarify an explanation. What do you mean by? What did you do in that bit? Can you show us what you mean by? Could you draw a picture of what you are thinking? (Communication and Participation Framework). | Learning Objectives: WALT find and describe the location of an object using coordinates. Curriculum Elaborations/ Big Ideas: Position & Orientation: The position, direction, and pathway of objects can be described using coordinate systems. |
Problem A: You have been given a secret code which you need to decipher to create a mystery picture. | |
Launch: Discuss what you learned from last week’s 2 tasks. What is important to remember when using a coordinate system (i.e. airplane/ horizontal then vertical). Work collaboratively. | |
Conjectures/ Possible Strategies/ Solutions | |
Possible Strategies: Seeing patterns and doing lines all at once. Colouring by colour. Colouring by line. | Misconceptions: Mixing up the x and y (i.e. flipping the coordinates around). Turning the graph paper around |
Additional strategies/misconceptions (that emerged during the lesson) | |
Generalising (How will we connect the strategies to the big idea?). Further examples to extend children's thinking (or simplify if required). (see last week) | |
Formative assessment: Link to Reflection Notes (not for public use) | |
Week: 9/10 | Curriculum Level: Lv 3 Area: |
Teaching Focus: Model and support the use of questions which clarify an explanation. What do you mean by? What did you do in that bit? Can you show us what you mean by? Could you draw a picture of what you are thinking? (Communication and Participation Framework). | Learning Objectives: WALT find and describe the location of an object using coordinates. Curriculum Elaborations/ Big Ideas: Position & Orientation: The position, direction, and pathway of objects can be described using coordinate systems. |
Problem A (on paper): Caleb is given a piece of paper by a mysterious creature. The mysterious creature tells him that if he follows the instructions, he will find a message. Use the mysterious creature’s instructions to help Caleb find the secret message. [Instructions/ Message] Problem B (using ipads): A mysterious creature has dropped some clues under some orange cones on the hard court outside Ako 3. It has left the cones in a grid like this: [4 by 4]. Mr J has asked for your help to decipher the message the mysterious creature has left behind. | |
Warm up: game of NSEW (possibly moving to NE, NW,etc). Have kids stand and face north, they need to turn to the direction stated by the teacher. If they fail to turn the right way, they sit out. Last standing wins. Equipment: 64 cones?? Instructions on sheets of paper. Launch for Problem A (on paper): What can someone tell us about this picture - what do you need to do to find the treasure chest? | |
Conjectures/ Possible Strategies/ Solutions | |
Possible Strategies: Plot correctly x and y point Guess and check. | Misconceptions: Flipping the coordinate around. Not understanding what the coordinate represents. Turning the graph paper around |
Additional strategies/misconceptions (that emerged during the lesson) Outdoor task: guess & check was the main form that groups used to find the messages under the spots however, when deciphering the message some learners grasped the concept of how coordinates work. | |
Generalising (How will we connect the strategies to the big idea?). Further examples to extend children's thinking (or simplify if required). Get children to volunteer to colour in a block on the whiteboard for a particular coordinate. Aeroplane analogy. | |
Formative assessment: Link to Reflection Notes (not for public use) Discussed how assessment could look in the future. Talked about using Fridays to do pre and post tests after certain topics. | |
Week: 7/8 | Curriculum Level: Lv 3 Area: Algebra (Linear) |
Teaching Focus: Ask the students to consider what steps they are doing over and over again and begin to make predictions about what is changing and what is staying the same. (Communication and Participation Framework). | Learning Objectives: WALT describe relationships between two variables. Curriculum Elaborations/ Big Ideas: • Create, continue, and predict further members of sequential patterns with two variables; • describe spatial and number patterns, using rules that involve spatial features, repeated addition or subtraction, and simple multiplication. |
Problem 1A: For the inter-zones rugby tournament this week, each child needed to bring $5 for the bus. Miss Va’afusuaga made this table to help her find out the total amount of money for the buses; [Number of kids vs $ table]. Problem 1a: Complete the table. Problem 1b: How could Miss Va’afusuaga create a graph to show the data which she collected for the bus money. Problem 1c: How could Miss Va’afusuaga create an equation to quickly find out more information. Problem B: Miss West and Mrs Moala were coding a pacman to collect coins. This graph shows the amount of coins the pacman collects on his journey.
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Resources: Basic Linear Functions; Functions (Input/Output Tables) Launch: Show videos and discuss Resources: new DMIC books, printed questions to glue into books, graph paper, rulers | |
Conjectures/ Possible Strategies/ Solutions | |
Possible Strategies (Week 7): TABLE: 5+5+5…= 5xn= Skip counting by 5’s GRAPH:
_Week 8______________________________________________ y=mx + b Language as used with kids: a = 3n + 25 (A= Amount and n=# of squares) Adding on in increments of 3 Independent variable on x axis(input)(horizontal); Dependent variable on y axis (output) (vertical). | Misconceptions (Week 7): -Not understanding how to write out an equation to explain what is happening mathematically. -Not understanding how to read a graph. -Not understanding how to draw a graph. -Not understanding how multiplicative thinking can be transformed into a graph. -flipping the variables. �___Week 8_____________________________________ -Not understanding that we started with coins (y-int) -Flipping the dependant and independent variables. |
Additional strategies/misconceptions (that emerged during week 7): -swapping the variables in a graph -making a bar graph -adding on instead of multiplying | |
Generalising (How will we connect the strategies to the big idea?). Further examples to extend children's thinking (or simplify if required). | |
Formative assessment: Link to Reflection Notes (not for public use) | |
Week: 6 | Curriculum Level: Lv 3 Area: Probability; Ratios |
Ask the students to consider what steps they are doing over and over again and begin to make predictions about what is changing and what is staying the same. (Communication and Participation Framework). | Learning Objectives: WALT model possible outcomes of one-stage chance situations. Curriculum Elaborations/ Big Ideas:
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Problem A: Kesaia, Victoria and Latisha were playing a game that had a spinner cut into 3 colours: red, yellow and blue. Each girl had to spin two times each turn. How many different colour combinations were possible for each turn? What is the probability that they will get the same colour on both spins? Problem B: Team 4 playing sports rotation: basketball, volleyball, rugby. Three rotations, how many combinations and what is the probability of a repeat rotation? | |
Warm up: Launch: Break down the word ‘combination’ Revise use of language: sort, arrange, combine, order, organise, 2 people playing to model it with heads and tails. What is probability? | |
Conjectures/ Possible Strategies/ Solutions | |
Possible Strategies: Use a tree diagram. Use blocks/colours to build and sort each combo List each combination (random selection) | Misconceptions: Use the same option more than once Not use a colour in a different location Get stuck on the names of the girls |
Additional strategies/misconceptions (that emerged during the lesson) | |
Generalising (How will we connect the strategies to the big idea?). Further examples to extend children's thinking (or simplify if required). Probability tree, Ratios, fair game Compare to last week: In last week’s scenarios, the colour (problem 1) or child (problem 2) could not be selected more than once. This week, they can. Compare the problems to discuss why this is. | |
Formative assessment: Link to Reflection Notes (not for public use) | |
Week: 5 | Curriculum Level: Lv 3 Area: Probability |
Teaching Focus: Model and support the use of questions which clarify an explanation. What do you mean by? What did you do in that bit? Can you show us what you mean by? Could you draw a picture of what you are thinking? (Communication and Participation Framework). | Learning Objectives: WALT model possible outcomes of one-stage chance situations. Curriculum Elaborations/ Big Ideas:
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Problem A: We have 4 bins outside the classroom: Red, Yellow, Black and Blue. How many different ways can we organise the bins so that they stay in the line against the wall? Problem B: John, Siosiua, Rae Jae, Kauri and Ozzy tried their best to be the fastest runner at an Eastern zones cross country competition. They all came in the top 5. In how many different ways could they cross the finish line? | |
Warm up: Launch: Break down the word ‘combination’ - pick out a number of kids (wearing different shorts: track pants, culottes, shorts) - how many different ways could they sit in the hall? | |
Conjectures/ Possible Strategies/ Solutions | |
Possible Strategies: Tree Diagram: Use blocks/colours to build and sort each combo List each combination (random selection) | Misconceptions: Use the same option more than once Not use a colour in a different location |
Additional strategies/misconceptions (that emerged during the lesson) Not understanding that if a choice has already been made, it cannot be made again. This will be different next week as the colour could come up in both situations. | |
Generalising (How will we connect the strategies to the big idea?). Further examples to extend children's thinking (or simplify if required). | |
Formative assessment: Link to Reflection Notes (not for public use) | |
Week: 4 | Curriculum Level: Lv 3 Area: |
Teaching Focus: Model and support the use of questions which clarify an explanation. What do you mean by? What did you do in that bit? Can you show us what you mean by? Could you draw a picture of what you are thinking? (Communication and Participation Framework). | Learning Objectives: WALT find a fraction of a set WALT find fractions of money Curriculum Elaborations/ Big Ideas: “Numbers can be partitioned and combined to solve more complex addition and subtraction and simple multiplication and division problems”�“Use a variety of types of numbers rather than just the ‘counting numbers’” NA3-5: Know fractions and percentages in everyday use. GM3-1: Use linear scales and whole numbers of metric units for length, area, volume and capacity, weight (mass), angle, temperature, and time. Math standards - geometry & measurement - use this explanation as our ceiling level. |
Problem A: Your group have been invited to go on a school trip with Mr Burt to Harvey Norman to purchase a new drone for Ako 3. The Amazeo Drone has a retail value of $835 and the Dynamo Drone has a retail value of $635. Mr Burt has a special school deal where he only pays 2/5 of the price of a drone of his choice. The total cost that Mr Burt pays for his drone is $254. Which drone did Mr Burt purchase? Problem B: Your group have been invited to go on a school trip with Mr Burt to Harvey Norman to purchase a new drone for Ako 3. The Fantastico Drone has a retail value of $75. Mr Burt has a special school deal where he only has to pay 4/5 of the price of a drone. The total cost that Mr Burt pays for his drone is $60. Explain why Mr Burt only has to pay $60 for the drone. | |
Warm up: Arm fractions: making relationships between different fractions. Launch: Building up the money using either physical money or a online/rewindable google drawing. Place materials out: times tables charts/ maths money | |
Conjectures/ Possible Strategies/ Solutions | |
Possible Strategies: Repeated Addition - guessing and checking ⅖ of 4835 = ? ⅕ of 835 = ? 835 divided by (split into) 5 equal pieces = ? Ones: 5 divided by 5 = 1 Tens: 30 divided by 5 = 6 Hundreds: 800 (80 tens) divided by 5 = 16 tens = 160 1 + 6 + 160 = 167 167 x 2 = 334 (OR 167 + 167 = 334) ⅖ of 635 = ? 635 divided by (split into) 5 equal pieces = ? Ones: 5 divided by 5 = 1 Tens: 30 divided by 5 = 6 Hundreds: 600 (60 tens) divided by 5 = 12 tens = 120 1 + 6 + 120 = 127 127 x 2 = 254 (OR 127 + 127 = 254) Draw a shape, cut into 5 pieces. Know that he got ⅖ off so he is paying ⅗ of the price. 835 split into 5 groups would be 100 in each space with 335 left so another 50 in each would be 750 used so 85 left which would split 10 more to each section making 800 used (160 in each) splitting the 35 into 5 groups would be 7 more for a total of 167 in each of the 5 groups. He will pay 167 +167=100+100=200 and 60+60=120 and 7+7=14 so $334 with being paid. | Misconceptions: Not understanding the related fractions e.g 1/5 and ⅖ goes with ⅘ and ⅗ to make a whole. Place value issues Not knowing how to partition the number to help with the multiplying of parts. Lack of times tables knowledge. |
Additional strategies/misconceptions (that emerged during the lesson) | |
Generalising (How will we connect the strategies to the big idea?). Further examples to extend children's thinking (or simplify if required). Make a link between fraction of a whole and fraction of a set.�Place value knowledge to solve hundreds. | |
Formative assessment: Link to Reflection Notes (not for public use) | |
Week: 3 | Curriculum Level: Lv 3 Area: |
Teaching Focus: Model and support the use of questions which clarify an explanation. What do you mean by? What did you do in that bit? Can you show us what you mean by? Could you draw a picture of what you are thinking? (Communication and Participation Framework). | Learning Objectives: WALT find a fraction of a set WALT find equivalent fractions. WALT find fractions of lengths Curriculum Elaborations/ Big Ideas: NA3-5: Know fractions and percentages in everyday use. GM3-1: Use linear scales and whole numbers of metric units for length, area, volume and capacity, weight (mass), angle, temperature, and time. Math standards - geometry & measurement - use this explanation as our ceiling level. |
Problem A: The Cook Island group had a shared lunch to celebrate Cook Island language week and they made minus. They had 3 kilograms of salad. One tenth of the salad was mayonnaise and three fifths of the salad was made from potatoes. How many grams of the salad was made from other ingredients? Problem B: The Cook Island group had a shared lunch to celebrate Cook Island language week and they made minus. They had 4 kilograms of salad. one eighth of the salad was mayonnaise and three fourths of the salad was made from potatoes. How many grams of the salad was made from other ingredients? | |
Warm up: Arm fractions: making relationships between different fractions. Launch and Norms: Make the connection of the word KILO- meaning 1000 of something. 1kg = 1000g. Make a connection to polygons where hexagon (hex means 6), for example. Ensure knowledge about fraction names e.g. ¼ = one quarter OR one fourth. | |
Conjectures/ Possible Strategies/ Solutions | |
Possible Strategies: Drawing out the fractions and labeling them. ⅗ = 6/10 3kg = 3000g 1/10 + 6/10 = 7/10 7/10 of 3000g = ? 3000g divided by 10 (3000 split equally into 10 equal groups) = 300g in each group. 300+300+300+300+300+300+300+300+300+300 = 3000g OR 300x10 = 3000g. Interested in 7 groups. 300 x 7 = 2100 g 3000-2100 = 900 g Therefore, 900 grams was made by the other ingredients. ⅗ = 6/10 3kg = 3000g 1/10 + 6/10 = 7/10 7/10 + 3/10 = 1 3/10 of 3000 grams (= the amount of other ingredients). 3000 divided by 10 = 300 grams 300 x 3 = 900 grams OR 300 Mayo: 1/10 of 3000 = 300g Potato: ⅗ of 3000 = ? 3000 divided by 5 = 600 g 600 x 3 = 1800 g 1800 + 300 = 2100g 3000g - 2100g = 900 grams Using decimals (kilograms) instead → answer will be 0.9kg | Misconceptions: Not understanding connections between kg/g. Not understanding the related fractions e.g 1/4 goes with 3/4 to make a whole. Not understanding that 3/5 is equivalent to 6/10 . Lack of multiplication knowledge. Not knowing that 3000g = 3kg |
Additional strategies/misconceptions (that emerged during the lesson) I noticed that...why did you do that? | |
Generalising (How will we connect the strategies to the big idea?). Further examples to extend children's thinking (or simplify if required). Make a link between fraction of a whole and fraction of a set. Make a link between adding different fractions (knowing 2/4 =½)�Make a link between g and kg (weight/mass). Bring in multiplicative thinking and decimal representations. | |
Formative assessment: Link to Reflection Notes (not for public use) | |
Week: 2 | Curriculum Level: Lv 3 Area: |
Teaching Focus: Model and support the use of questions which clarify an explanation. What do you mean by? What did you do in that bit? Can you show us what you mean by? Could you draw a picture of what you are thinking? (Communication and Participation Framework). | Learning Objectives: WALT find a fraction of a set WALT find equivalent fractions. WALT find fractions of lengths Curriculum Elaborations/ Big Ideas: NA3-5: Know fractions and percentages in everyday use. GM3-1: Use linear scales and whole numbers of metric units for length, area, volume and capacity, weight (mass), angle, temperature, and time. Math standards - geometry & measurement - use this explanation as our ceiling level. |
Problem A: For the Beep Test last week, John ran 1km. Siosiua ran half of John’s distance and Miss West ran a quarter of John’s distance. How many metres did Siosiua and Miss West run altogether? Problem B: For the Beep Test, John ran 1.5 km. Siosiua ran two quarters of John’s distance and Miss West ran three quarters of John’s distance. How many metres did Siosiua and Miss West run all together? | |
Warm up: Arm fractions: making relationships between different fractions. Launch: Reminder that 1km = 1000m. Ensure knowledge about fraction names e.g. ¼ = one quarter OR one fourth. | |
Conjectures/ Possible Strategies/ Solutions | |
Possible Strategies: ¼ + 1/2 = ¾ ¾ + ¼ = 1 whole 1km = 1000m 1/4 of 1000m = 250m, so 2/4 (½) must = 500m and ¾ must be 750m. ¾ of 1 = 1000m divided by 4 = 250m 250x3 = 750m ½ of 1 = ? 1000m divided by 2 = 500m ¼ of 1 =? 1000m divided by 4 = 250m 500 + 250 = 750m 1km = 1000m 3/4 of 1000 = 750m (see above for working) 1000-750 = 250m So 1/4 of 1km = 250m 1/4 of 1 = 0.25km So 2/4 (½) of 1 = 0.5km And 3/4 of 1 = 0.75km | Misconceptions: Not understanding connections between km/m. Not understanding the related fractions e.g 1/4 goes with 3/4 to make a whole. Not understanding that ½ is equivalent to 2/4. Not understanding that ½ + ¼ = ¾ |
Additional strategies/misconceptions (that emerged during the lesson) | |
Generalising (How will we connect the strategies to the big idea?). Further examples to extend children's thinking (or simplify if required). Make a link between fraction of a whole and fraction of a set. Make a link between adding different fractions (knowing 2/4 =½)�Make a link between m and km (distance). | |
Formative assessment: Link to Reflection Notes (not for public use) | |
Week: 1 | Curriculum Level: Lv 3 Area: Fractions/ Measurement |
Teaching Focus: Model and support the use of questions which clarify an explanation. What do you mean by? What did you do in that bit? Can you show us what you mean by? Could you draw a picture of what you are thinking? (Communication and Participation Framework). | Learning Objectives: WALT find a fraction of a set WALT find fractions of lengths Curriculum Elaborations/ Big Ideas: NA3-5: Know fractions and percentages in everyday use. GM3-1: Use linear scales and whole numbers of metric units for length, area, volume and capacity, weight (mass), angle, temperature, and time. Math standards - geometry & measurement - use this explanation as our ceiling level. |
Problem A: The Matariki Light Trail in GI is 1 kilometre long. Miss West and Mrs Moala walked ⅗ of the trail. How many metres did they still have to walk to reach the end? Problem B: The Matariki Light Trail in GI is 1 kilometre long. Miss West and Mrs Moala walked ¾ of the trail. How many metres did they still have to walk to reach the end? | |
Launch: Be clear with how long a km is. Maybe pull up google maps to measure length of school to the beach. Measure school to the train bridge = ~1km. Measure school to the beach = ~ ½ a km (500m). Does it look like half? Making a clear link between km and m. | |
Conjectures/ Possible Strategies/ Solutions | |
Possible Strategies: ⅗ + ⅖ = 1 whole 1km = 1000m ⅕ of 1000m = 200m, so ⅖ must = 400m. 1km = 1000m ⅗ of 1000 = 600m (see above for working) 1000-600 = 400m So ⅖ of 1km = 400m ⅕ of 1 = 0.2km So ⅖ of 1 = 0.4km And ⅗ of 1 = 0.6km | Misconceptions: Not understanding connections between km/m. Not understanding the related fractions e.g ⅖ goes with ⅗ to make a whole. |
Additional strategies/misconceptions (that emerged during the lesson) Fold back to ¾ as the fraction to support learners with the concept of finding a fraction of a set. | |
Generalising (How will we connect the strategies to the big idea?). Further examples to extend children's thinking (or simplify if required). Make a link between fraction of a whole and fraction of a set.�Make a link between m and km (distance). | |
Formative assessment: Link to Reflection Notes (not for public use) | |