Embedded Files
Core concept: Halfway is the same distance from 2 ends of a length.
Warm-up/Daily number sense: One more and one less – 10 minutes
Warm-up/Daily number sense: One more and one less – 10 minutes
Build student understanding of numbers before and after by exploring a number track.
Build student understanding of numbers before and after by exploring a number track.
Draw a large number track from 0–21 on a piece of paper or whiteboard or use numeral cards.
Draw a large number track from 0–21 on a piece of paper or whiteboard or use numeral cards.
Roll a large 20-sided die or use a virtual dice. Ask students to state the number that is one more or one less than the number rolled.
Roll a large 20-sided die or use a virtual dice. Ask students to state the number that is one more or one less than the number rolled.
Select a student to indicate on the number track the number on the dice. Ask the student to point to and identify the number one more or one less. Have the student state the number and then state the number one more or more or one less. For example, the number is 16 which is one more than 17, or the number is 4 which is one less than 5.
Select a student to indicate on the number track the number on the dice. Ask the student to point to and identify the number one more or one less. Have the student state the number and then state the number one more or more or one less. For example, the number is 16 which is one more than 17, or the number is 4 which is one less than 5.
Repeat the above steps to consolidate the skill of identifying the number after or before a given number, without needing to count from one.
Repeat the above steps to consolidate the skill of identifying the number after or before a given number, without needing to count from one.
Activity: Hit the target – 20 minutes
Activity: Hit the target – 20 minutes
Tell 2 students to stand facing each other approximately 2–3 metres apart. Give each student 3 beanbags. Place a paper plate target between the 2 students, deliberately ensuring it is not placed in the middle, or at the halfway point between the 2 students. Explain the aim of the game is to throw the beanbag as close to the paper plate target as possible. The student whose beanbag is the closest will be awarded a point and each student will have 3 turns.
Tell 2 students to stand facing each other approximately 2–3 metres apart. Give each student 3 beanbags. Place a paper plate target between the 2 students, deliberately ensuring it is not placed in the middle, or at the halfway point between the 2 students. Explain the aim of the game is to throw the beanbag as close to the paper plate target as possible. The student whose beanbag is the closest will be awarded a point and each student will have 3 turns.
Ask students to throw their first beanbag.
Ask students to throw their first beanbag.
This is likely to have one of the students state that the game is not fair.
This is likely to have one of the students state that the game is not fair.
Move the paper plate very close to this student. Ask students to throw their second beanbag.
Move the paper plate very close to this student. Ask students to throw their second beanbag.
The other player is likely to state that it is not fair.
The other player is likely to state that it is not fair.
Facilitate a class discussion about why the students think the game isn’t fair.
Facilitate a class discussion about why the students think the game isn’t fair.
How can we make the game fair?
How can we make the game fair?
What needs to change? Explain your thinking.
What needs to change? Explain your thinking.
Tell students that the target needs to be at the halfway point between both students.
Tell students that the target needs to be at the halfway point between both students.
Ask students to turn and talk to a partner about how the halfway point could be found. Ask students to share some of their thinking and strategies.
Ask students to turn and talk to a partner about how the halfway point could be found. Ask students to share some of their thinking and strategies.
Provide students with a selection of concrete materials.
Provide students with a selection of concrete materials.
For example, interlocking cubes or pipe cleaners.
For example, interlocking cubes or pipe cleaners.
Ask students to work with their partner to find the halfway point between the 2 players. Students may explore informal measurement ideas to measure the length between the 2 players, including counting how many steps or how many interlocking cubes. Have some students share their thinking.
Ask students to work with their partner to find the halfway point between the 2 players. Students may explore informal measurement ideas to measure the length between the 2 players, including counting how many steps or how many interlocking cubes. Have some students share their thinking.
Model marking where the 2 players are standing and use a string line to measure from one student to the other student, ensuring that the string is pulled tight and straight. Place a peg on the piece of string and model folding it in half to identify the halfway point.
Model marking where the 2 players are standing and use a string line to measure from one student to the other student, ensuring that the string is pulled tight and straight. Place a peg on the piece of string and model folding it in half to identify the halfway point.
Using the halfway point, place the paper plate down as the target. Discuss with students the fairness of the game now that the halfway point has been determined.
Using the halfway point, place the paper plate down as the target. Discuss with students the fairness of the game now that the halfway point has been determined.
Provide the opportunity for all students to play the game and determine the halfway point between players.
Provide the opportunity for all students to play the game and determine the halfway point between players.
Activity: Finding half – 15 minutes
Activity: Finding half – 15 minutes
Ask students to form one line. Have students think about how to find the halfway point of the class line. Ask some of the students to share their thinking.
Ask students to form one line. Have students think about how to find the halfway point of the class line. Ask some of the students to share their thinking.
Ask a student to recreate the line using interlocking cubes. Model breaking the line of interlocking cubes into 2 equal parts, lining the 2 halves up next to each other. If there are an uneven number of students, break the model into halves and identify the one left over.
Ask a student to recreate the line using interlocking cubes. Model breaking the line of interlocking cubes into 2 equal parts, lining the 2 halves up next to each other. If there are an uneven number of students, break the model into halves and identify the one left over.
Tell students the model will be tested for accuracy. Ask the first students at each end of the line to sit down. Then ask the next students from each end to sit down. Repeat until the last one or the last 2 students are standing. Explain to students that if there are 2 students standing at the end, the class can be split evenly into half. If there is one student standing at the end, the class cannot be split evenly into a half.
Tell students the model will be tested for accuracy. Ask the first students at each end of the line to sit down. Then ask the next students from each end to sit down. Repeat until the last one or the last 2 students are standing. Explain to students that if there are 2 students standing at the end, the class can be split evenly into half. If there is one student standing at the end, the class cannot be split evenly into a half.
Discuss and connect the mathematics – 10 minutes
Discuss and connect the mathematics – 10 minutes
Provide a selection of concrete materials and ask students to create a model representing the line of students. Ask students to identify the halfway point and break the model in half.
Provide a selection of concrete materials and ask students to create a model representing the line of students. Ask students to identify the halfway point and break the model in half.
Make connections from a previous lesson when students were using streamers to find the position of halfway, more than halfway or less than halfway on a whole length. Ask students:
Make connections from a previous lesson when students were using streamers to find the position of halfway, more than halfway or less than halfway on a whole length. Ask students:
What is the halfway point? Explain your thinking.
What is the halfway point? Explain your thinking.
How did you find the halfway point with your streamers? How was this different or the same as finding the halfway point in the game?
How did you find the halfway point with your streamers? How was this different or the same as finding the halfway point in the game?
How will we check that we found the halfway point for our game?
How will we check that we found the halfway point for our game?
What is the difference between a half and halfway? How do you know?
What is the difference between a half and halfway? How do you know?
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