Grade 3 Number and Algebra Section A - Number and Place Value 1 Journal problem 1 Numbers to 100 Problem 1, Lesson 1: Novel problem You will need: a large number of bundling sticks and some rubber bands for this problem. Each student should also have a place value chart (see appendix 1). Prior to introducing the problem, the students should have some experience placing sticks onto the place value chart. Demonstrate by adding one stick at a time until there are ten. Ask the students what the problem is with having 10 sticks in the ones column, and what they can do about it. Take suggestions and then explain that they can no longer stay in the ones column. Demonstrate how to make a bundle of ten sticks and place the bundle in the tens column. Ensure that the students understand that there is now one ten and there are no ones on the chart. Continue to add sticks until another bundle is made and placed in the tens column. Students should also be familiar with the hundred board and have used it for counting numbers to 100. Before you begin, give each student a pile of sticks making sure there are more than twenty. This activity is also found in the Grade One Thinking Journal. Leading questions: How could you find out how many sticks you have? Count how many sticks you have. How can you be sure that you count each stick only once? How many bundles of ten can you make? How many are left over? Put the bundles and left over sticks onto the place value chart. Which column do they go in? How many sticks do you have? Can you find that number on the hundred board? How could you work out what number is ten more/less than your number? Try counting back/forward from your number. Watch out for: Some students may want to count the sticks in the tens column rather than the number of bundles (e.g. They may say I have 20 tens when there are two bundles of ten). Ensure that students understand that they have 20 sticks or two bundles of ten. Students may need help relating the sticks on the place value chart to a number. If this happens, call an extra sharing time to discuss how to do this before asking them to locate the number on the hundred board. Teaching Tips: If students do not understand that the number that is ten less/more than their number will be in the same position on a line before/after, encourage them to count back or forward and question them about the position of the number they finished at. Differentiation: Students requiring support: See Counting and ordering numbers in What students need to know and understand about number p26 Ensure that students understand the concepts associated with counting Provide further opportunities for students to make numbers to one hundred using bundling sticks and place either sticks or numbers onto a place value chart.
Grade 3 Number and Algebra Section A - Number and Place Value 2 Provide further opportunities to locate numbers on a hundred board and use it for counting on from a given number. Extension: Encourage students to find some other ways to represent the number of sticks they have been given. Students could be asked to compare their number with the numbers that other students were given (e.g. find someone with a number that is bigger, smaller or the same as yours). Students could write their number onto a piece of paper and then form small groups to arrange themselves in order according to the numbers they have. Problem 1, Lesson 2: Manipulation, application and practice Teacher information: The Manipulation Problem asks students to find other ways to represent the number 38. They may like to draw different groupings of fudge (e.g. two lots of ten and 18 single pieces) or write the number in digit or word form. Provide bundling sticks or other concrete materials as needed. You will need: containers with up to a hundred objects, place value charts (appendix 1), bundling sticks, rubber bands, ordinary dice or ten-sided dice, cards with a number of ten frames (appendix 2), counters and a timer. Hands-on activities and games to choose from: Give students a container with a large number of objects (less than 100) and ask them to first guess how many there are and then count them. Students work in pairs to play number games: - Use the place value charts and bundling sticks. Students roll a die and add the number of sticks indicated to their chart. Once they have ten or more sticks they make a bundle of ten to place in the tens column. Play continues for a specified amount of time. When the time is up, the students compare the number of sticks they have and decide who has more. - Students place counters on a card with tens frames according to the number that is Tips for parents: Count stairs, letter boxes, trucks etc as opportunities arise. Ask your child to count and sort larger numbers of items. Ask questions like How many muesli bars do I have if there are three packets of muesli bars that have ten in each and four single muesli bars? Talk about larger numbers up to 100 as they occur (e.g. House numbers on long streets). indicated by a roll of a die. They fill up each frame before starting on another. Play continues for a specified amount of time. When the time is up, the students compare the number of counters they have and decide who has more. Puzzles that match numerals with pictures of groups of objects or match groups arranged in different ways. Students can make their own puzzles to give to a friend to solve. Differentiation: Students requiring support: Consider mixed ability grouping to ensure students having difficulties receive assistance from more capable students during hands-on activities. Give students 38 bundling sticks or other concrete materials and ask them to organise them in first in 3 tens and 8 ones and then in other ways. Extension: Encourage students to find as many different ways to represent 38 as possible.
Grade 3 Number and Algebra Section A - Number and Place Value 3 Try doing the same for other two-digit numbers. Later they could order them from smallest to biggest. Problem 1, Lesson 3: Backwards problem, reflection and extension Before you begin: Students should be familiar with the hundred board and have used it for counting. In order to solve the problem, students will have to visualise the board and understand how the numbers are arranged. What to look for: Students should use the numbers that have been written on the hundred board to help them to locate the other numbers. The numbers in the larger row will be simpler as students can count on in ones to work them out. The other numbers will be more challenging as some students may not have the understanding that the number directly above a specified number will be ten less. Differentiation: Students requiring support: If students are unable to visualise how the numbers on the hundred board are arranged, allow them to look at the board to help them fill in the numbers. Take the numbers off a hundred board or have tiles with the numbers to 100 written on them. Ask students to replace the numbers on the board or place the tiles in order. Cut up paper copies of hundred boards into different shaped pieces and have students work out how they fit together. Extension: Provide other examples of parts of hundred boards for students to complete. Give fewer clues to help them.
Grade 3 Number and Algebra Section A - Number and Place Value 4 Problem 1: Numbers to 100 How many bundling sticks did your teacher give you? Make as many bundles of 10 sticks as you can and tie them together with rubber bands. How many bundles How many sticks of 10 did you make? are left over? Tens Ones 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Draw the bundles and sticks on the place value chart. Colour in the square on the hundred board that shows the number of sticks you have. 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 Put a cross on: The number after your number The number before your number The number that is 10 more than your number The number that is 10 less than your number Problem solving: Teacher initials: Date: Student solved the problem with: o Minimal help o Some prompting o Solved after explanation o Did not work out a solution by themself N/A not a novel problem o Name: Peer Assessment Tell your partner what you have found out about your number.
Grade 3 Number and Algebra Section A - Number and Place Value 5 Application questions Mike Mike s class is going to sell fudge at the school fete. Some fudge will be sold in bags of 10 pieces. Some pieces of fudge will be sold separately. This is the fudge that some of Mike s classmates made. How many pieces of fudge did each person make? Write the number of pieces of fudge that each person made. Jessica Jordan Mary Who made the most fudge? Who made the least fudge? Write the numbers in order from the least to the most fudge.
Grade 3 Number and Algebra Section A - Number and Place Value 6 Manipulation problem Jordan made some fudge for the fete and packed it ready to sell. Some fudge was in packets of 10. Here is how his fudge was packed. What other ways could Jordan have packaged his fudge? or Write or draw some different ways that the fudge could have been packed. Backwards question This is part of a hundred board that has been cut out and some numbers have been lost. What numbers are missing? Write the numbers that are missing from the piece of 100 board. 36 48 53 54 56 59