When was the last time you encountered a math problem that looked like this: ¾ ÷ ¼?

Was it in a college math class? Or maybe back in high school or middle school? Do you remember how to solve it?

Now think about what types of math you use in your daily life. Sometimes a recipe calls for ¾ cup of sugar, but you can only find your ¼ measuring cup. How many scoops do you need to make ¾? This is the same problem as ¾ ÷ ¼, but seems much easier to solve because of the context involved. The situation helps the math make sense.

This understanding and application of math to real-life situations is referred to as numeracy or quantitative literacy. A numerically literate, or numerate, individual can use mathematics in everyday life and understand and appreciate the information presented in mathematical terms (Cockcroft, 1982). They can make sense of the sugar problem above, able to calculate a 20% tip, or understand what “buy one, get one 50% off” means at a store.

Word Problems and Numeracy

Using word problems in math teaching is critical to building numeracy skills.

How many of us were taught the procedure to solve ¾ ÷ ¼, without understanding that we were being asked how many ¼ scoops are in ¾ of a cup? Whether you were taught “copy, dot, flip”, “keep, change, flip”, or “invert and multiply”, there was most likely very little understanding as to why you were performing that procedure, or what types of situations you might need to apply this trick. When procedures are taught without context, some students may get the right answer, but they miss out on the chance to become numerate. Problem solving as the introduction to mathematics shows students the relevancy and the necessity of math in everyday life and allows students to apply their learning to new and different mathematical situations.

Tips: How to Incorporate Meaningful Problem Solving

One important strategy is to start learning with problem-solving. Many textbook programs will wait to introduce word problems until the end of the lesson or even the end of the unit. Students can build understanding and numeracy by solving problems from the start. Find or create problems that students can relate to and that they can model. If the situation or context of the story problem makes sense to students, they will be able to use objects or drawings to solve it. Follow the three guidelines below to improve problem-solving in your classroom this semester.

Action

Make sure there is action on the problem whenever possible, especially when introducing a new concept. Problems with clear action tend to be easier for students to visualize and solve.

  • Action: 18 students are playing on the playground. 12 more students run over to join them. How many students are on the playground now?
  • No action: There are 18 bananas and 12 apples on a table. How many pieces of fruit are on the table?

Real and Relevant

Make the situation realistic and relevant to students’ lives and experiences. Some of the word problems you find in textbooks are outdated and can be confusing. Not many students use stamps or have coin collections nowadays!

  • Josie wants to save up to $850 to buy a new phone. By doing chores and saving birthday money, she now has $623. How much more money does Josie need?
  • Kenny loves to watch lizards at the zoo. In one exhibit he saw 3 lizards. He was so excited to see the zookeepers adding 7 more lizards into the exhibit while he was there. How many lizards are in there now?
  • I have 925 followers on one social media app. I have three times that amount on a different app. How many followers do I have on the second app?

Build Complexity

Start with simple numbers and build up to more complex ones.

  • Beginning: We need a fence around our school garden. The garden is 3 feet wide and 6 feet long. How many feet of fencing do we need to buy to surround the entire garden?
  • Later in the learning sequence: We added 2 new garden plots. The first is 12 feet wide by 7 feet long and the second is 13 feet wide by 9 feet long. How many feet of fencing do we need to surround both garden plots?

 

A numerically literate, or numerate, individual can use mathematics in everyday life and understand and appreciate the information presented in mathematical terms (Cockcroft, 1982).

 

Connecting Problem-Solving to Procedures

One important role the teacher plays during problem-solving is to help students see their thinking in more formal mathematical terms. When a young student uses cubes to solve an addition problem, for example, the teacher can help them write an equation that matches their strategy, introducing the addition and equal signs, along with the correct way to write the numerals. When a student uses a strategy that involves the commutative or associative property to add numbers in a different order, the teacher can call attention to that and spark a discussion among the students about why this works, and if it always will work. Students will not magically know certain vocabulary words, or how to use parentheses, and the teacher’s role is to help students understand and apply the formal mathematics behind their thinking as they move toward more abstract procedures and algorithms called for in their grade level standards.

Creating Better Problem Solvers Every Day

Parents will often tell their child’s teacher, “I’m not a math person.” or “I hated word problems growing up.” Many teachers also hear, “When are we going to use this?” in class each day. Building numeracy through problem-solving can help to develop strong problem-solving skills and the ability to see math as a tool for approaching everyday situations. Try incorporating realistic, relevant word problems more often, and watch your students grow into confident, numerate mathematicians who will say “I’m a math person!” and “I love word problems!”

Works Cited

Cockcroft, WH: (1982) Mathematics Counts: Report of the Committee of Inquiry into the Teaching of Mathematics in Schools

Get started today!

Are you ready to embark on a journey towards literacy excellence? Contact us to learn more about our programs and how we can support your school’s literacy and numeracy development.

Absolutely!