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You’re starting a new topic in your math intervention small groups.
You know that you want to build UNDERSTANDING in your students rather than just “showing them how to [insert topic here].
You know that math intervention is so much MORE than doing a worksheet together at a small group table.
So how do you anchor and start your lesson?
Lesson Introduction Strategies
While there are infinite ways to start a lesson, leaning into the Math Practice Standards can give you meaningful inspiration. In this post, we will look at three example lesson anchors that match the standards. Use these as a jumping-off point for your own math lessons!
- Make Sense of Problems and Persevere in Solving Them
- Look For and Express Regularity in Repeated Reasoning & Construct Viable Arguments and Critique the Reasoning of Others
- Use Appropriate Tools Strategically
Making Sense of Problems and Persevering in Solving Them
This lesson comes from the Kindergarten Math Intervention Unit Exploring Addition.
In this lesson, students will transfer their knowledge of the part/whole language and the number bond in order to begin adding blocks together. This is a step towards addition as your students will be working with numbers and the part/whole relationship. We are NOT yet introducing the + sign.
Rather than teaching our students a procedure to complete when they see the + sign we are instead focusing on the action of addition. The + sign as a shortcut to represent this action.
Tell your students a math story “I bought a few flowers at the store this morning. I bought 3 red roses and 2 yellow daisies. I’m wondering how many flowers would be in my bouquet if I put all of the flowers together.“
Begin by showing your students a stack of 3 red blocks and a stack of 2 yellow blocks. Put the stacks into the parts of the double number bond template . Ask your students what they see and what they notice. How do these blocks match your story? Ask your students what they might do to find the WHOLE number of flowers in your bouquet.
Push the blocks together into the whole and count to find the whole.
Next, ask your students to describe what happened with the blocks and as they describe record numbers into the second number bond. Ex: Part of our flowers were red. How many flowers were in the red part of our bouquet? 3! So we will put a 3 in our number bond. And how many flowers were in the yellow part of our bouquet? 2! Where do you think we could represent the 2 yellow flowers in our number bond? Yes! In the other part! And how many flowers were in the whole bouquet? 5, yes! We put the 3 part and the 2 part together and it made 5 flowers.
By grounding your students’ earliest experiences with addition within a story context you are lending CONTEXT and MEANING to the skill of addition while also BOOSTING your students’ problem solving skills!
Look for and Express Regularity in Repeated Reasoning & Construct Viable Arguments and Critique the Reasoning of Others
This activity comes from the 1st grade math intervention unit 10 More and 10 Less Mental Math
Adding or subtracting 10 to a given number is a place value standard, NOT an operation standard. If you look at the first-grade CCLS, most addition strategies are listed under the OA Operations and Algebraic Thinking strand- but not this skill! Building a frame of thinking around adding and subtracting 10 or 1 allows students to deepen their understanding of place value.
To start this activity, dump out a pile of ten sticks and ones base ten blocks onto your table. Write the number 35 on a teacher whiteboard. Give each student their own whiteboard with the number 35 at the top. Ask students to build this number from ten sticks and ones.
After each student has built this number, ask students “What would I need to do to my blocks if I wanted to add ten more?” As you ask this question, note “+10” after the 35 on your whiteboard. Students might ask you to add ten ones but if they do, ask immediately if there is a more efficient way to add 10. After you have all arrived at the conclusion that students should add a ten stick to show ten more, have each student do just that; add 1 ten stick to their blocks and then note 35 + 10 = 45 on their whiteboard.
Ask students to look at their whiteboard and circle the number that shows how your blocks started and then what the blocks looked like after ten was added.
Ask students to note what has changed between these two numbers and what has stayed the same. If they respond by saying something like “The 3 changed to a 4 but the 5 is still a 5,” push them to be more precise about what the 3, 4 and 5 refer to in the problem. For example, “We started with 5 ones and when we added ten we still had 5 ones.” “We started with 3 tens but when we added a ten then we had 4 tens”.
Now that you have set the stage, this is the time for your students to look for patterns and construct an argument around what happens when you add a ten to a number!
Ask students if they can state a rule about what happens to the tens and ones when we add ten. The rule should sound something like “When we add ten, the tens change but the ones stay the same”. I like to name the rule after the student (ex: Shaina’s Rule) who ultimately made that statement- even if it was with prompting! Record this rule on the white board next to the 35 + 10 = 45 equation with the student’s name.
Next, ask each student to pick a number between 11 and 89 and tell them that they will be using their number to test “Shaina’s Rule”. Each student would then work independently to build their number, record it on their white board, add ten with a ten stick, record the equation and solution and write what stayed the same and what changed when they added ten. After each student completes this process, go around the table asking each student if “Shaina’s Rule” worked with their number and how they knew being sure to look for place value language.
Use Appropriate Tools Strategically
This activity comes from the 3rd Grade Math Intervention Unit Distributive Property Multiplication. In this lesson, students are going to use square tiles to model the distributive property. Starting a lesson can be as easy as describing a math concept and asking students “Could you use [specific math tool] to show this idea?”
In this lesson your goal is to help your students to see that they can put arrays together to solve a larger multiplication problem. All arrays in this lesson will revolve around x2 facts which are likely known and comfortable for your students.
Begin by telling your students the following story:
I am laying square crackers out on a tray. I made 2 rows with 5 crackers in each row. It didn’t look like quite enough crackers, so I added two more row of crackers. How many crackers are on the tray in all?
As a group, guide your students to model this story using square tiles. First lay out 2 rows of 5 square tiles. Pause and ask your students “How many crackers do we have on our tray right now? Let’s write a multiplication equation that matches our crackers.”
Next, use a new color of square tiles to model the remainder of the problem in adding another two rows of crackers. Again, ask your students to examine the new part. “How many crackers did we add to our tray? Let’s write a multiplication equation that matches the crackers we added.”
Next, ask your students to examine the entire tray as a whole and to make a prediction around the total number of crackers on the tray. Some students may immediately recognize that 10 + 10 = 20 and that there are a total of 20 crackers.
Finally, ask your students to write an equation that matches the entire array. Demonstrate, on a white board, for your students how the entire equation 4 x 5 = 20 can be decomposed and written as (2 x 5) + (2 x 5).
DO NOT ask or expect your students to write this equation or show this notation at this time. Your goal in this unit is for your students to start to notice what happens when multiple arrays are combined. Adding in the notation at this point will likely cause your students to start thinking about these problems from a procedural light. By thinking aloud and demonstrating you are simply are connecting the abstract equations to your students thinking – planting seeds for future instruction.
