(I couldn t find a Smartie Book) NEW Grade 5/6 Mathematics: (Number, Statistics and Probability) Title Smartie Mathematics Lesson/ Unit Description Questions: How many Smarties are in a box? Is it the same amount for every box of Smarties? Does the Smartie Company put the same amount of each colour of Smartie in each box? Are some Smartie colours more popular than others? If we added all the colours together for the whole class would one colour be more represented than another colour? Do the Smartie colours follow any particular pattern? Connections to Mathematics Program of Studies General Outcome Number Develop number sense Specific Outcomes (Processes) Grade 5 Demonstrate an understanding of fractions. Relate decimals to fractions and fractions to decimals. Grade 6 Demonstrate an understanding of percent (limited to whole numbers) concretely, pictorially and symbolically. Statistics and Probability Collect, display and analyze data to solve problems. Grade 5 Construct and interpret double bar graphs to draw conclusions. Grade 6 Graph collected data and analyze the graph to solve problems 1
Lesson: The students will each receive a large box of Smarties. They will count and sort the contents of their individual boxes by colour. They will record their data individually and calculate the fractions and percentages of each colour to the total Smarties in each box. They will use a calculator to do this. They will then put all the Smarties back in the box. A class wide demonstration of bar graphs using the whole class data is performed. Discussion is ongoing about prediction. Average number of Smarties per box was calculated (grade 7 outcome). Average number of each colour was calculated. The relationship of the number of grams in a box compared to the number of Smarties in the box was also calculated. Each student will then record their information numerically and present their findings on a bar graph and pie chart. The students will be asked to predict how many Smarties of each colour they should get if they took a sample of 20 from the box. The students then shake the box of Smarties and count our 20. This is a random sample. They record the fractions for each colour and compare this to the predicted fraction. The students presented their information on poster board. Teacher Notes Identification of prerequisite skills Rounding (estimation) skills and some background in fraction concepts both set models and whole number models are useful. Counting up to 60 is required. Suggestions and considerations for successful lesson implementation. The students are not allowed to eat the Smarties until all of the required data has been collected. This typically can be done in one period. The summarization, calculation and compilation of data can be done after the fact. The students counted their Smarties on paper towels and washed their hands prior to touching them. There is to be no sharing of Smarties. Ideas for extension and enrichment - Students had to insure that the individual colour percentages that they calculated totaled 100%. This presented some difficulty. Students who were more competent were asked to identify the computational errors that could have occurred which would have resulted in a total different than 100%. They were then asked to calculate their percentages to more decimal places to see if they could obtain a more precise answer. This really tested their rounding skills. The less skilled students were told to round their percentages to the nearest whole number and assistance with that was provided. The more competent students could understand why the individual percentages needed to total 100%. The bar graphs could all be done on the computer using Excel. Students who need extra reinforcement could use a variety of manipulates to 2
reinforce their understanding of set models interlocking cubes and area models - fraction circles etc. This activity took the class about 4 full class periods. Lesson/Unit Materials and Resources Handouts bar graph templates, recording charts, Pencil crayons, calculator Chart paper for compilation of class results colored markers for recording class results box of Smarties per student Student Handout Attached. Assessment Class discussion and individual observation of student results provided much insight into their understanding of fractions, percentages and sampling. At this grade level (Grade 5 and 6), full understanding of some of the concepts is not required. The objective is to introduce students to the manipulation of data, visual representation of data and how to analyze data. However, several key numbers indicated whether they had an understanding of set models and area models. Did the sum of the fraction numerators for each colour equal the total number of Smarties in the box or the sample? Did the students understand why?. Did the sum of the individual percentages for each colour equal 100%. Were the students able to order their fractions from smallest to largest? In the overall compilation of class results, there was much discussion about the fact that each colour was represented equally. Discussion of the process of manufacturing Smarties and the opportunity to discuss economics followed. 3
Smarties: Recording Sheet - Total Box Name: Bar Graph Represent each Smartie that you have on the recording sheet by colouring in one square starting at the left. Total 1. How many Smarties were counted altogether? 2. What fraction of your Smarties was purple? 3. Which were the two least common Smarties colors? 4. What fraction of this group are primary colors? How did you find your answer? 5. In looking at your bar graph and the graphs of others in your group, what patterns do you see? 6. How would this graph change if all of the pink Smarties had been removed before you had begun this activity? 4
Recording Sheet Two Sampling (not eating Yet) Of the twenty candies with which you will be working, estimate how many of each colour you think you will have once you count them. Use your bar graph from Recording Sheet One to estimate. Shake up your box of Smarties to mix them up. Now open the box and count out twenty (random sample). PLEASE KEEP THEM OUT OF YOUR MOUTH! Count the actual number of each color in your group of twenty. Record your findings. How many of each color did you count? Write your results as a fraction of a set or group. Order the Smarties colors from least to greatest with 1 being the Smarties color that was most common and 8 being the Smarties color that was least common. Smarties Color Estimate (in a group of 20) Actual (in a group of 20) Fraction of the Group Order From Most to Least Use the data you collected from your twenty Smarties to create a bar graph that shows the number of each colour. 5