This unit integrates the mathematics and science learning areas, and provides an opportunity for students to explore the context of chemical reactions involving common household acids and bases. In turn, students will develop their use of rates and ratios, and will explore linear relationships using tables and graphs.
The activities in this unit develop students' mathematical skills and knowledge, relevant to their multiplicative thinking and understanding of patterns and relationships, in the context of science (understanding the material world; investigating the chemical properties of acids and base).
Within this, students utilise a scientific investigation to model a real life situation. This includes the following key understandings:
Note that the context of neutralising acids and bases does not yield the exact linear relationships hinted at in this unit, but does so approximately when only strong acids and bases are used. It can be argued that students will gain a better understanding of chemical processes overall, if they can first look for clear patterns in such constrained settings.
The work outlined in the practical activities requires solutions and equipment that should be available in secondary school laboratories. You will need to have access to the expertise of a science teacher (or other, knowledgeable community members) and the resources necessary for this practical work.
This cross-curricular, context-based unit has been built within a framework that has been developed, with input from teachers across the curriculum, to deliver the mathematics learning area, whilst encouraging differentiated, student-centred learning.
The learning opportunities in this unit can be further differentiated by providing or removing support to students, and by varying the task requirements. Ways to differentiate include:
With student interest engaged, mathematical challenges often seem more approachable than when presented in isolation. Therefore, you might find it appropriate to adapt the contexts presented in this unit.
The first session is an introductory activity that is aimed to spark the imagination of students, to introduce the need for a particular idea or technique in mathematics that would enable them to explore deeper into that context. It is expected that rich discussion may be had around the context and around the nature of the mathematics involved.
Following the introductory session, each subsequent session in the unit is composed of four sections: Introducing Ideas, Building Ideas, Reinforcing Ideas, and Extending Ideas.
Introducing Ideas: It is recommended that you allow approximately 10 minutes for students to work on these problems, either as a whole class, in groups, pairs, or as individuals. Following this, gather the students together to review the problem and to discuss ideas, issues and mathematical techniques that they noticed during the process. It may be helpful to summarise key outcomes of the discussion at this point.
Building Ideas, Reinforcing Ideas, and Extending Ideas: Exploration of these stages can be differentiated on the basis of individual learning needs, as demonstrated in the previous stage of each session. Some students may have managed the focus activity easily and be ready to attempt the reinforcing ideas or even the extending ideas activity straight away. These could be attempted individually or in groups or pairs, depending on students’ readiness for the activity concerned. The students remaining with the teacher could begin to work through the building ideas activity together, peeling off to complete this activity and/or to attempt the reinforcing ideas activity when they feel they have ‘got it’.
It is expected that once all the students have peeled off into independent or group work of the appropriate selection of building, reinforcing and extending activities, the teacher is freed up to check back with the ‘early peelers’ and to circulate as needed.
Importantly, students should have multiple opportunities to, throughout and at the conclusion of each session, compare, check, and discuss their ideas with peers and the teacher, and to reflect upon their ideas and developed understandings. These reflections can be demonstrated using a variety of means (e.g. written, digital note, survey, sticky notes, diagrams, marked work, videoed demonstration) and can be used to inform your planning for subsequent sessions.
The relevance of this learning can also be enhanced with the inclusion of key vocabulary from your students' home languages. For example, te reo Māori kupu such as āwhata (scale), āwhata pH (pH scale), kauwhata (graph), and tūhuratanga ā-ringa (practical investigation) might be introduced in this unit and then used throughout other mathematical learning.
This activity is intended to motivate students towards the context and to inform teachers of students' understandings.
The Bee Sting Problem:
One summer’s day Charlie’s little sister Lilly comes running into the house, crying. She has been stung by a bee! There is no consoling Lilly. Charlie remembers something he heard once about how he can add some household ingredient to take the pain away...but what was it? And why? And how much?
What can you find out about bee stings?
This session focuses on learning about household acids, bases, and neutral solutions.
Introducing Ideas
Building Ideas
Reinforcing Ideas
Make up solutions of each of the following and test with cabbage juice indicator to decide whether they are acids, bases or neutral:
Extending Ideas
From your research you have learned that bee stings are acidic.
This session focuses on learning about pH indicators.
Introducing Ideas
The pH scale goes from 1-14, representing the concentration of hydrogen ions (H+) in a solution. A solution which has a pH of 1 has 10x more hydrogen ions (H+) than the same volume of a solution of pH of 2. A solution which has a pH of 1 has 100x more hydrogen ions (H+) than the same volume of a solution of pH of 3.
Building Ideas
Reinforcing Ideas
Extending Ideas
This activity aims to develop students’ understanding of a science concept through interpretation of a mathematical relationship displayed on a graph. The relationship itself is exponential, but is applicable for students working at level 4 of mathematics in the NZC because the numbers are used are whole numbers from 1-14 and the powers of ten.
This session focuses on making a pH indicator scale.
Introducing Ideas
Building Ideas
Reinforcing Ideas
Extending Ideas
This activity has an emphasis on practical technique for science, with the need for careful measurement and recording being a major outcome. Encourage students to take accurate measurements and to record their results in a table. If time and resources allow, they should repeat the procedure several times so that they may use the average of their individual results for each test tube.
This session focuses on students graphing the results of their practical investigations.
In session four, students gathered data from a practical investigation, measuring the quantity of a given basic solution needed to neutralise an acidic solution. This investigation was modelling how much of a sting treatment (base) would be needed to to neutralise different amounts of a bee sting (acid).
Introducing Ideas
Building Ideas
Reinforcing Ideas
Extending Ideas
This session focuses on interpreting and applying graphed results of a practical investigation.
In session five, students graphed their data from a practical investigation, measuring the quantity of a given basic solution needed to neutralise an acidic solution. This investigation was modelling how much of a treatment (base) would be needed to to neutralise different amounts of a bee sting (acid). Their graphs should show a linear relationship between the amount of sting (acid) and the amount of treatment (base) needed to neutralise the sting.
Introducing Ideas
Building Ideas
Reinforcing Ideas
Extending Ideas
This session focusses on the generalisation and application of a linear relationship. Because the relationship has been derived from a practical context, students should be well placed to discuss the domain and range of the relationship. Looking at the shape of the graph, they should recognise a linear trend. Their data may not fit exactly along the trend-line, which will give the opportunity to discuss experimental uncertainty and the accuracy of their measurements. Discussion could compare the relative merits of using their graph (interpolation, extrapolation) with the use of the algebraic rule of the trend-line to solve a problem.
Dear families and whānau,
Recently, we have been developing our use of rates and ratios, and exploring linear relationships using tables and graphs, in the context of chemical reactions involving common household acids and bases. Ask your child to share their learning with you.
Printed from https://nzmaths.co.nz/resource/bee-sting-problem at 8:43pm on the 27th April 2024