One of the traps I think we can fall into when teaching Grades 5 and 6 is believing that because the math is becoming more complex, the learning needs to become more abstract too. But our older primary students still benefit enormously from hands-on learning.
In fact, I found the opposite approach often got the best results. When learning felt a little more like play, a challenge or an investigation, my students were more engaged, but that didn’t mean the math was any less rigorous.
When I taught Grade 5, I started the year with hands-on number sense investigations, just as I had done in my younger classrooms.It gave me a chance to revisit some of those foundational skills we can easily assume students have mastered, while also pushing their mathematical thinking much further. And once again, it set us up beautifully for the rest of the year.
Students were investigating patterns, reasoning, discussing their ideas, working with large numbers and making connections. Those number skills then became something they could draw on as we moved into more complex math.
So if you’re teaching Grades 5 or 6, don’t pack away the hands-on learning just yet!
Here are eight Grade 5 and 6 number sense investigations that keep students actively thinking about numbers without simply handing them another worksheet.
What does number sense look like in Grades 5 and 6?
Number sense doesn’t disappear when students reach the upper grades. It becomes more sophisticated.
We want students to work flexibly with much larger numbers, compare and order them, estimate and round, reason about their position on a number line and understand the properties and relationships that exist between numbers.
This is also where we can really start exploring the patterns within our number system through factors, prime and composite numbers, square numbers and triangular numbers. And I deliberately call many of these investigations. We aren’t always telling students exactly what mathematical rule to apply. We’re giving them something to explore and asking:
- What do you notice?
- What pattern can you see?
- Why do you think that happens?
- Can you prove it?
That’s where the really interesting math conversations begin. Here are 8 activities to get your Grade five and Grade six students investigating numbers.
1. Take Number of the Day into BIG numbers
Number of the Day certainly isn’t just for younger students. In Grades 5 and 6, give students a five-, six- or seven-digit number and ask them to pull it apart in as many ways as possible.
They can decide whether it’s odd or even, expand it, add and subtract 10 and 100, represent it on a place value chart, write it in words and work with the digits to create the smallest and largest possible numbers. This is such an easy warm-up to come back to throughout the year because you simply change the number.
5-digit numbers might be enough challenge for some students, while others can move into 6- and 7-digit numbers.
2. Number line mysteries reasoning challenge
By Grades 5 and 6, plotting a number on a clearly labelled number line isn’t enough.Instead, take some of the information away: Give students the beginning and end of a number line, perhaps one midpoint, and a mystery point.
Now ask: What number do you think belongs here? Explain your thinking.
What I love about Number line mysteries. is that the answer is only half the task. Students need to reason about scale, intervals and relative position and then explain how they know. You can have students work independently first and then compare their reasoning with a partner. Then they can have some really great mathematical conversations:
- Did they use the same strategy?
- Did they estimate differently?
- Can one student convince the other?
Now a simple number line investigation has turned into a mathematical discussion.
3. Ask students to judge someone else’s estimation
Instead of constantly asking students to round a number, give them two possible estimates and ask: Which one is more accurate?
For example, students might see:
322 + 401with two suggested estimates: 720 or 740
Their job isn’t simply to calculate the exact answer. They need to decide which estimate makes more sense and explain the thinking that could have been used to get there. I love this because it shifts rounding away from being a rule students mechanically follow. They need to think about reasonableness. And that’s really what estimation is for.
Teacher tip: Get students working in pairs and insist that they justify their choice. A disagreement between two students can lead to some fantastic math talk!
4. Let students DISCOVER triangular numbers
This is where these activities start feeling much more like genuine investigations. Rather than beginning with a definition of triangular numbers and then giving students questions to answer, let them investigate the pattern.
Students use visual dot representations to build and extend triangular numbers. They can start with a given triangular number, draw what comes next and look for what changes each time.
Then we can ask:
- What do you notice?
- How is the pattern growing?
- Can you predict the next triangular number without drawing it?
- Could you work out whether ANY number is triangular?
This is exactly the kind of math I love for older students, they aren’t being handed a rule and asked to practise it. They’re discovering the rule.
5. Become a Square Number Detective
You can take a very similar investigative approach with square numbers.
Start visually by giving students a dot representation and ask them to investigate how the pattern grows. Then have them test numbers to determine whether they’re square numbers and look for patterns in what they discover.
Just like the triangular number investigations, students can gradually move from concrete and visual representations towards much more abstract reasoning. And this is such a good example of why I don’t think upper-primary math needs to begin with abstraction. The visual isn’t making the learning “easy,” it is giving students something they can reason from. Once they see the structure, they’re in a much better position to describe and generalise it mathematically.
6. Hunt for prime numbers
Prime numbers are perfect for an investigation because students can actually go looking for them.Start with a number chart and ask students to identify which numbers they believe are prime.
Students begin testing numbers, looking at their factors and noticing what makes a prime number different.
This activity is deliberately open-ended so students can investigate what a prime number is and identify primes on a number chart. Later activities introduce factors more explicitly and ask students to use that understanding to decide whether individual numbers are prime or composite.
Instead of: “Here’s the definition of a prime number. Memorise it.” – we’re moving towards: “Here’s a collection of numbers. What can you discover?”
7. Explore the “magic” of prime and composite numbers
Once students understand prime and composite numbers, we can start having some real fun with them. Prime and Composite Magic investigations are designed to take students further into these number properties and help them discover some of the patterns and “magic” hiding within the math.
This is the type of activity I particularly love in Grades 5 and 6 because students often don’t feel as though they’re completing a traditional math task. They’re looking for something and testing an idea. And yet underneath all of that engagement is rigorous mathematical thinking about factors, primes, composites and number properties.
It’s a good reminder that learning feeling like play and learning being rigorous are not opposites. Our older students can absolutely have both.
8. Finish with math debates, challenges and games
One of the best ways to find out whether students really understand a mathematical idea is to ask them to defend it. Once students have completed some of the investigations, bring them together for collaborative challenges.
Ask them to state their case and debate a mathematical point of view using what they’ve learned. Give them a challenge where they need to break the rules and test their number understanding.
Hands-on doesn’t mean “easy”
This is probably the biggest thing I want teachers to take away from this post. Hands-on learning isn’t something students should grow out of.
Somewhere along the way, we can start associating hands-on math with younger children and written, abstract work with older students. But hands-on doesn’t have to mean counting bears and blocks.
For a Grade 5 or 6 student, hands-on learning might mean investigating a number pattern, testing possibilities on a hundreds chart, solving a mystery, sorting and comparing numbers, debating an idea with a partner or physically marking patterns to see what emerges.
The thinking can be incredibly rigorous, and they’re much more likely to be engaged than if we’ve handed them another page of questions to complete.
Use investigations to see how your students THINK
Starting the year with these number sense investigations also gave me something incredibly valuable as a teacher.Information!
When students are completing a worksheet, we often see whether they got something right or wrong but when they’re investigating, we can see so much more.
As grade 5 & 6 teachers we are trying to look at how our students think mathematically, which gives you so much useful information for where your teaching needs to go next.
Want these Grade 5 & 6 number sense investigations ready to go?
If you’d like to bring more hands-on learning into your upper-primary math lessons without having to create all the investigations yourself, we’ve done the prep for you.
Our Grade 5 & 6 Number Sense Investigations includes activities covering place value, comparing numbers, number lines, rounding and estimation, triangular and square numbers, prime and composite numbers, as well as collaborative challenges, games and opportunities for assessment. The activities can be used with the whole class, in math rotations or in small groups for intervention or extension.
Many are designed to be used in write-and-wipe sleeves or with mini whiteboards too, so students can come back to them again and again.
Most importantly, they’re designed to get students thinking, discussing, investigating and investigating the number system.
Grab your copy of the Grade 5 & 6 Number Sense Investigations HERE.
Rainbows ahead 🌈
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About the Author: Ashleigh Smith
Ashleigh Smith is an experienced primary educator, former school leader and Co-Founder of Rainbow Sky Creations. With almost 20 years in education, Ashleigh has taught in Australia and internationally in Dubai, UAE. Today, she draws on her classroom and leadership experience to create practical, engaging resources that save teachers time and make learning meaningful and fun. A passionate cheerleader for teachers, Ashleigh is all about helping educators work smarter, not harder. She also co-hosts the Rainbow Skies for Teachers podcast, sharing practical ideas, strategies and encouragement with primary teachers around the world. Connect with her on Instagram or LinkedIn.
