Think Board 2 Solve problems by using number sentences for addition or subtraction. a Think Board to link different ways of representing addition and subtraction problems including words, concrete materials, pictures and number sentences. This will assist them in solving word problems that contain unknown quantities. Proficiency Strand: Problem Solving – using number sentences that represent problem situations; formulating problems from authentic situations. students to find connections between the different ways of representing a problem. This helps students to focus on the meaning of the operation rather than on just calculating to find an answer. Model working through a word problem using the Think Board. Progress from MAG 2.2.5 where students were using the standard addition and subtraction word problems. Introduce students to the word problems that have an unknown quantity embedded in the question. completed Think Board. Annotate comments made by the student that demonstrate their understanding of the connections between the different ways of representing the problem. Check to see if students select the correct operation, select a suitable representation, and correctly represent the number sentence. solve questions from NAPLAN while using the Think Board. Concrete Materials – counters, unifix, bundle sticks Whiteboard pens Word problems – unknown quantity embedded (Dark Blue) Set of Think Board Cards Early Years FISH Kit TOPIC CONTENT KEY IDEA Pre-ASSESS ASSESSMENT INVESTIGATION STUDENT JOURNAL RESOURCES 2.3.2 Number 2 ACMNA026 Investigate number sequences, initially those increasing and decreasing by twos, Students will practice skip counting in 2s, 3s, 5s and 10s from any number as a starting point using a hundreds board. Proficiency Patterns on a Hundreds Board. The following strategy is a mental routine designed by Ann and Johnny Baker (2006). This process consists of Closed, Open, and Flip questions. Give each student a 100s Fill in the missing numbers in the pattern Print and laminate a series of skip counting patterns with numbers missing from the Senteacher website. Provide washable markers and ask students to figure our the skip pattern and fill in the missing numbers. Students should be Calculators: With the use of a calculator ask students to find the counting pattern for the 20s, 50s and 100s. Discuss the similarities and differences 100s board Mini whiteboard Whiteboard markers
threes, fives and ten from any starting point, then moving to other sequences. Describe patterns with numbers and identify missing elements. Strand: Fluency – counting numbers in sequences readily Understanding – connecting number calculations with counting sequences. board and washable pen. Ask the following questions, and observe student responses. Scaffold the responses to assist students in finding the patterns in number sequences. able to fill in the missing numbers, as well as describe the pattern, for example: this is counting in 4s. Achievement Standard: Recognise increasing and decreasing number sequences involving 2s, 3s, 5s. between the 2s, 5s, and 10s. Source: Department of Education, Queensland. 1991. Years 1 to 10 Mathematics Sourcebook: Activities for teaching mathematics in Year 3. Department of Education: Qld p40. TOPIC CONTENT KEY IDEA Pre-ASSESS ASSESSMENT INVESTIGATION STUDENT JOURNAL RESOURCES 2.3.3 Place Value 3 ACMNA028 Group, partition and rearrange collections up to 1000 in hundreds, tens and ones to facilitate more efficient counting. Students will partition numbers into hundreds, tens and ones, and regroup collections as necessary as a quantity is added. Proficiency Strand: Understanding- Partitioning and combining numbers flexibly. Place Value Chart Write hundreds, tens and ones on the columns of the show-me frame place value chart. Write a 3-digit number on the board, for example 19 Ask the students to represent the number using tiny hundreds, tens and ones on top of the frame. Place the corresponding place value arrow beneath the frame. Achievement Standard – count to and from 1000. Say a three-digit number and ask students to represent this number using place value arrows. Students record this number using hundreds, tens and ones, expanded notation and numeral. Select a number. Write clues for it and then create a WANTED number poster. Source: Baker, J. & Baker, A. 2006. Natural Maths Strategies Book 2. Blake Education: Clayton. P 69 Tiny ones, tens and hundreds Place value arrows Mini-whiteboard Digits Show me pocket frame Place Value dice – 100s, 10s,1s FISH Kit TOPIC CONTENT KEY IDEA Pre-ASSESS ASSESSMENT INVESTIGATION STUDENT JOURNAL RESOURCES 2.3.4 ACMNA031 Recognise Achievement Standard : Represent multiplication and division by Give students 5 bowls. Ask Mini Whiteboard
- Doubling and represent as repeated addition, groups and arrays grouping into sets. Use a Target game to assess students ability to work forwards and backwards with doubling by filling in the spaces. Cut squares of paper in half to create triangles. Write the answer at the top of the triangle and the number that you are doubling in each of bottom corner. Show students only the bottom two numbers and ask them to double, reveal the top of the triangle for the answer. students to place one counter in each bowl and record this multiplication fact 5 x 1 = 5. Ask students to then place 2 counters in each bowl and record this multiplication fact 5 x 2 = 10. Continue until students have placed ten counters in each bowl. Ask students to explain the patter to you. • Whiteboard pens • Counters • Dominoes • Doubles Poster • FISH Kit TOPIC CONTENT KEY IDEA Pre-ASSESS ASSESSMENT INVESTIGATION STUDENT JOURNAL RESOURCES 2.3.5 - Arrays ACMNA031 Recognise and represent as repeated addition, groups and arrays. Students will understand the commutative property of multiplication using an array model. Proficiency Strand: Understanding – identifying and describing the relationship between addition and subtraction and multiplication and division. Understanding – Activity Process – Rows Give each student 12 counters. Ask students to arrange counters into equal rows. Ask students: “How many different ways can you arrange counters into equal rows?” Allow students time to record and share their answers. Repeat with a larger or smaller collection of objects. Activity Process – Turnarounds Place and array on a felt square e.g. 4 rows of 2. Use the large rubber bands to highlight the rows. Write: 4 Observe students when playing the Match Me game. Note their ability to find the matching cards and give an answer to the algorithm. Achievement Standard – Represent multiplication and division by grouping into sets. Counters Felt Squares Large rubber bands Rods Calculator FISH Kit
halves, quarters and eighths of shapes and collections. number of parts to the size of a fraction. counters. 3. Ask students: How would we work out how many is half of these counters? 4. Model with the students the dividing of counters into two grouping circle, thus making Half. 5. Record the fraction in written form, explaining where the numbers have come from and if we add the two halves back together they would equal the beginning number. 6. Repeat with different numbers of counters. Achievement Standard: Divide collections and shapes into halves, quarters and eighths. given six. How many lollies would there have been altogether? Or Sam had half of the toy cars. He had 5 cars. How many cars altogether? Allow students to use hands on materials to solve problems. TOPIC CONTENT KEY IDEA Pre-ASSESS ASSESSMENT INVESTIGATION STUDENT JOURNAL RESOURCES 2.3.7 Number Patterns 2 ACMNA026 Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and ten from any starting point, then moving to other sequences. ACMNA035 Describe patterns Students will copy, continue, create and describe patterns with numbers. Activity Process – Explore Patterns on Hundreds Board. Ask students to make a yellow, yellow, red patterns on the 1-100 hundreds board. Remove all the red counters, revealing skip counting in threes. Discuss the pattern observed, for example: Diagonal patterns, the digits add up to 3, 6 or 9. Students complete a number pattern on the Number Pattern Base Board – given a rule and a starting number. *Students identify the rule – given a completed number pattern. *Students identify missing elements of a number pattern – given the rule and missing numbers in the pattern. Achievement Standard – Identify the missing element in a number sequence. Mathswire website provides growing patterns as introduction to algebraic principles. Students should draw and/or describe the next couple of stages in the pattern and create an input/output table to describe the relationship between the stage and the number of blocks used. Students should be challenged to Double sided counters 1-100 Hundreds board (A3) Number Pattern Base Board Calculator Whiteboard Makers
with numbers and identify missing elements. Proficiency Strand – – connecting number with counting sequences. Proficiency Strand: – connecting number with counting sequence. Discuss the rule that has been used to create the number pattern – add 3. Repeat for skip counting in 2s and 4s; 5s – observing the pattern of the last digits; Repeat for 10s observing the pattern created – what is changing?(the first digit). What is staying the same? (the last digit). write a rule in words and more capable students should be challenged to write a general mathematical rule that would calculate the number of blocks needed for any given stage. TOPIC CONTENT KEY IDEA Pre-ASSESS ASSESSMENT INVESTIGATION STUDENT JOURNAL RESOURCES 2.3.8 3D Objects ACMMG043 Describe the features of three objects. Proficiency Strand: Problem Solving – Making models Students will describe the features of objects, draw them and use materials to make models of these. Activity Process – Sorting and Constructing 3D Objects. Hold up a cube and review the properties. Use the terms ‘faces’, ‘edges’ and Hold up a rectangular prism. Compare and contrast the Observe the students as they discuss the properties of shapes in activity process A and B. Display the 3D objects: Sphere, cube, prism, cylinder, cone; pyramid. Select a shape and ask the students to name the object and describe two properties, for example: It’s got a circle shaped based and one edge. It’s a cone. This could be done as a transitional activity. Boxes: Provide each student with a sheet of coloured card. Ask students to create a container without a lid that is suitable for carrying 1 cup of sand. Source: First Steps in Mathematics – 3D Objects: Sphere, cube, prism, cylinder, cone. Mystery box – Cardboard box about 25x25x35cm with a lid. Cut holes in each side (leaving a flap) as in the diagram Straws, string, craft paper and sticky tape: to construct models of 3D objects.
2 and order several shapes and objects based on length, area, volume and capacity using uniform informal units. Proficiency Strand: Fluency – using units iteratively to compare and compare volume and capacity using a variety of uniform informal objects, discussing and sharing their findings. measurement. Gather materials: A container, water, sand, marbles, unifix. Explain to student that you want to find the best way to measure the capacity of a container (how much it holds). Fill one container with the blocks or marbles. Ask: Is the container full? Are there any spaces? How can we prove that there are spaces? Suggest adding water to prove this. Now fill the container with water. Ask: Is the container full? Are there any spaces? Repeat with sand. Discuss the most appropriate materials to use for measurement. Discuss the advantages and disadvantages of each material, for example: The unifix blocks leave many gaps. extension activities – Comparing Containers. Ask students to journal their understandings about measurement from this activity. Note students’ understanding of Uniform units of measurement Appropriate materials for measurement of capacity Using the same unit of measure to make comparisons Ordering containers according to their capacity. 20 spoonfuls of rice. What might the container that I used look like? Do student look for a range of container and do their estimate improve as they continue to look? As an extension for this activity, ask students to make a container our of card that will hold the 20 spoonfuls of rice. ice-cream bucket, teapot, water bottle, baking tray, jugs, ice cube trays and margarine containers. Coloured water Pebbles or marbles Unifix blocks Sand Measuring cup, egg cup medicine cup, tablespoon.