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How to cultivate a growth mindset in your math classroom black and green text with a big leaf

Cultivating a growth mindset in your math classroom is more than the cheerleading of "try harder, you got this!" While that is important, it's not everything.  If you present a problem to a student, and there is only one right way to accomplish the problem with only one correct solution, and all you say is try harder, the student may hit a wall, and if they are truly stuck and they can't get over the wall, then there they will stay . Teaching math as one strategy and one solution promotes a fixed mindset.

Students need more than one path.  Either another strategy to do the problem, which eventually will lead to the same solution.  Or another path to do the problem, which eventually leads to a different (although still correct) solution.  This promotes a growth mindset. I created this lovely visual to better explain.

Fixed Mindset vs Growth Mindset

one path and wall to show a fixed mindset two paths and one solution and two paths and two solutions to show a growth mindset

If you are not sure which type of problems to give your students, I have some that I created with this in mind. These Back-to-School activities were created for students to problem-solve and be successful.  They are back-to-school themed, but would work great for anytime of year.   With a low floor and high ceiling, these would work for a 6th, 7th, or 8th grade classroom.  

Here are some other great activities to incorporate a growth mindset in your classroom.  

math mindset questionnairemathematical growth mindset activity growth mindset posters


pin image includes text how to cultivate a growth mindset in your math classroom with a leaf calculator and pencil

The best 7th grade math homework

Quality math worksheets are hard to find for your 7th grade math students.  If you try googling 7th grade math worksheets you will likely get worksheets that are 20 fluency math problems and that's it.  While fluency is important, it is definitely not everything. That's why I created these 7th grade math worksheets that are based on understanding one math concept in three different ways plus a review section.

Review: All math in 7th grade is built on previous math concepts.  Many times students need a refresher of these math concepts.  That's why I included review problems of essential concepts.

Fluency: Like I mentioned, fluency is important, but it's not everything.  These worksheets contain about 6 problems to check fluency of the math concept. 

Application:  Applying the math skill to real-world problems is essential.  Students need to be able to problem-solve and apply their skills to real-world concepts.  Every worksheet includes at least 3 real-world questions. 

Analysis: These are a variety of different type of problems.  They can be error-analysis, or creating their own problem with a specific answer.  The purpose of these problems is to check for conceptual understanding.  

If you are looking for some quality math worksheets for your 7th grade classroom you might want to check these out.  They are perfect for review, homework, and in-class work.  

7th grade math homework for 11 topics to increase fluency and conceptual understanding


7th grade math homework to increase fluency and understanding

I had never even heard of Algebra tiles until my third year of teaching.  Our school invested in a bunch of Algebra tiles, and I quickly had to learn how to use them.  I tried searching the internet to understand how to use these with my students...but I couldn't find a lot of information.  So I took some time at my desk alone with my blocks and started figuring these things out...and it was like gold.  So awesome in so many ways. Suddenly integers, solving equations, simplifying expressions, factoring trinomials, and multiplying binomials made so much sense.  When I used Algebra tiles in my classroom I was able to reach all students.  They are magic! Today I am going to share with you how to use Algebra tiles to teach multiplying binomials.  

Start by reminding your students how to find the area of a rectangle.  Connect the fact that when you multiply two factors together you also are calculating the area of a rectangle with the factors as the side lengths.  Polynomials work the same way.  If you are given the factors (x + 2) and (x + 3), those are the side lengths of a rectangle, with the product as the area.  

Algebra tiles showing x^2 + 5x + 6 as a rectangle with side lengths x + 2 and x + 3
  • Students line up the factors to represent the length and width.  
  • Students fill in the the area with blocks that are the same length and width as the blocks on the sides of the space they are trying to fill.  
  • Once the space is filled they will have a rectangle.
  • Students will see what blocks are in the area space of their rectangle, and that's the product of the binomial factors.  
Algebra tiles showing 2x^2 + 5x + 2 as a rectangle with side lengths x + 2 and 2x + 1Algebra tiles showing x^2 + 5x + 4 as a rectangle with side lengths x + 1 and x + 4

If you need some activities to practice multiplying binomials in your middle school math classroom you can check out these products below.  Click on the photo for more details.  
Factoring and Multiplying Polynomials Stations      Factors and Models with Algebra Tiles Task Cards

If you don't have Algebra tiles for your classroom you can use these printable ones.

Algebra Tiles Printable FREE

x^2+5x+6 factored using algebra tiles

Calculating the area of composite figures and shapes is an important skill for middle school math students.  Some students will pick up on this skill quickly, and others will need various methods taught to them so they understand.  Read on to learn how to teach and challenge ALL OF YOUR STUDENTS to make sense of area of irregular shapes. 

Review:  Review how to calculate the area of shapes such as triangles and rectangles.  Make sure that students understand that height and base must be perpendicular. 

Divide:  Divide the area up into different triangles and rectangles (or parallelograms).  Students will often have different ways to divide up the composite shape.  Let them divide it up differently and compare answers. 

Negative Area:  Composite area can also be determined by taking a larger area and taking away a negative area (an area that is not actually part of the composite shape).  Take a look at the image below.  To determine the area of the L-shaped blue section, a student can determine the area of the larger square (blue) and take away the away of the negative smaller square (yellow).  This method is good to at least show to students as it will be a good skill for them to understand as they progress in mathematics. 
large blue square minus a smaller yellow square equals the area of a L shape inside a square

Problem Solving:  I ALWAYS try and incorporate problem-solving into any lesson.  With composite figures, provide shapes with sides that are not marked, but can be determined by problem-solving.  Compare Figure A and Figure B below.  To determine the area of the composite figure below, most students will determine the area of the 6 x 7 rectangle and the additional triangle.  Notice in Figure A that all dimensions to determine the area of the rectangle and triangle are given.  In Figure B the height of the triangle is not as clear.  Students would have to problem solve that the perpendicular height of the triangle is 10 - 7 = 3.  This is also a way to differentiate in your classroom.  Some students may be ready to problem-solve quicker than other students, and that is ok. 

Composite shapes with dimensions

If you are looking for a fun way to practice composite area in your classroom take a look at this fun activity  This area of composite figures worksheet is an engaging activity which includes two versions.  One version has all the measurements listed.  The other versions has missing measurements that can be determined through problem-solving.

Area of Composite Figures Activity


pin for 4 strategies of composite shapes

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