Anyone who has seen Happy Numbers in action can tell that students love it. But what do teachers think? One compliment we often receive is that Happy Numbers offers a diverse range of activities. By presenting the same concept using a variety of tools, students are given the opportunity to investigate concepts thoroughly. Another is that the math itself is what piques student interest, rather than a separate, unrelated game thrown in as a reward for enduring a set of dry math problems.
These are two great reasons to use shopping-based exercises throughout your math instruction. At Happy Numbers, we don’t treat shopping as a separate topic, but strategically integrate it throughout our curriculum to target key skills. For example, students don’t jump right from combining coins to making change. Instead, each of these skills is presented sequentially along with similar skills that use different representations (e.g., base-10 blocks, equations, hundred chart). This way, the shopping exercises relate to student learning and students are equipped with the skills they need to succeed.
Shopping is an authentic, mathematical activity that calls on a wide range of skills. It’s also fun! Even if you’re not using Happy Numbers, this post will give you ideas about how to scaffold shopping exercises to meet students’ needs at various levels. You can re-create shopping exercises in the classroom using plastic coins and images with prices written on them. If your class does use Happy Numbers, of course the scaffolding is built right into our program and students will even receive immediate feedback and support as they work through each activity.
Here’s how we use shopping activities to scaffold math skills…
All of the exercises mentioned here are part of the HappyNumbers.com course and are presented along with exercises using other representations.
1. Begin with the simplest addition skills.
As soon as students are able to add two numbers on their own, we present them with the first shopping exercise. Here, students choose two numbers (not coins) out of three to reach a given sum:
All sums are 10 or lower, and students have already worked extensively adding small numbers using objects, the number line, and equations. Now they can enjoy practicing their new skills with number bonds while “buying” treats.
2. Increase the challenge to more complex addition.
Next, we keep the shopping experience the same, but present students with more challenging addition in two ways. The first challenge is to simply purchase items with higher prices (up to 20):
The next challenge at this step is to use three addends to reach a given sum (again, up to 20):
As you can see, these first three shopping exercise increase in difficulty quite a bit, which is why we don’t recommend presenting them to students in immediate succession. There is quite a bit of math that goes on between each of these exercises in order to prepare students to succeed with each task.
3. Use coins to reach a given sum.
Once students are familiar with adding numbers to reach a sum, we introduce the constraint of using only certain “coins”. (We use a more universal labeled coin to focus on numeracy rather than coin recognition.) We begin with just 10s and 1s – a structure familiar to students from their work with base-10 blocks and the hundred chart. At this point, we also increase the total sum to accommodate the use of more tens:
After students demonstrate mastery with 10s and 1s, we introduce 50s and 5s to achieve the same task:
Here, it is interesting for teachers to observe students’ strategies. Will they continue adding 10+10+10+10+10+10 or will they discover the “shortcut” of using 50+10? What will they do if they run out of 1s? To ensure students try both options, we eventually limit the number of certain coins. This way, students realize they don’t have enough and must use a higher denomination.
4. Count a collection of given coins.
As students progress in this topic, we reverse their role – instead of choosing coins to reach a given total, they now have a given set of coins and must determine the total. In essence, they’ve gone from the role of customer to that of cashier.
Again, we begin the exercise by using only 10s and 1s:
Then we increase the complexity by including 5s:
The final challenge at this step is to count a given collection of coins and then compare that with several given totals. Students love figuring out which toy they can afford! This exercise is more open-ended (just like real shopping) because there are several possible correct and incorrect responses.
At this point, if a student selects a toy that is lower than the given amount, we recommend they do not yet calculate the change. This is a more advanced two-digit subtraction skill that we’ll address later on. On Happy Numbers, students are shown the coins that make up their change, but they are not asked to count them or calculate it.
5. Find the total of multiple items.
Moving toward increasingly authentic shopping experiences, students next use coins to pay for two items:
They have been well-versed in two-digit addition up to this point, so they have multiple strategies available to them in solving each problem:
– Add the two numbers in their head and pay for the total
– Pay for one item, then the next item without totaling
– Pay for all the 10s first, then all the 1s
Since the second strategy doesn’t require mental addition, we don’t let students rely on it too long. Again, we limit their coin selection so they must find the total instead of using the “pay for one then pay for another” trick:
Again, our emphasis is on number values rather than actual coin recognition, which is why we’ve chosen to include 2s here and not 25s.
Next, we ensure students use mental two-digit addition by removing the coins and focusing just on the two items and the total. You can present this task as one in which students choose two items and find the total or, as we’ve done, give students the total and have them determine the two items that were purchased. The latter approach, in which they must figure out what the cat bought, seems to really hold their interest:
6. Complete the entire shopping process.
Finally, students are well-prepared to take on every step in an authentic shopping experience:
a) Count your money and choose items to purchase.
b) Present the items to a cashier and choose coins with which to pay.
c) Determine the amount of change owed and count it out. (Too bad this cashier didn’t use Happy Numbers or he could do it himself!)
d) Enjoy the rewards of your successful shopping trip!
As you can see, these shopping exercises increase in difficulty quite a bit, which is why we spread them across grade levels and lessons rather than presenting them in immediate succession. Happy Numbers carefully integrates all of these steps, and the prerequisite skills needed, to give students deep conceptual understanding of math.
We’ve found that shopping exercises give students great practice with meaning. We hope you’ll give them a try in your classroom. Kids love them and you’ll love them, too!
Evgeny & Happy Numbers Team